phd problem statement in computer science

A new ‘AI scientist’ can write science papers without any human input. Here’s why that’s a problem

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Karin Verspoor receives funding from the Australian Research Council, the Medical Research Future Fund, the National Health and Medical Research Council, and Elsevier BV. She is affiliated with BioGrid Australia and is a co-founder of the Australian Alliance for Artificial Intelligence in Healthcare.

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Scientific discovery is one of the most sophisticated human activities. First, scientists must understand the existing knowledge and identify a significant gap. Next, they must formulate a research question and design and conduct an experiment in pursuit of an answer. Then, they must analyse and interpret the results of the experiment, which may raise yet another research question.

Can a process this complex be automated? Last week, Sakana AI Labs announced the creation of an “AI scientist” – an artificial intelligence system they claim can make scientific discoveries in the area of machine learning in a fully automated way.

Using generative large language models (LLMs) like those behind ChatGPT and other AI chatbots, the system can brainstorm, select a promising idea, code new algorithms, plot results, and write a paper summarising the experiment and its findings, complete with references. Sakana claims the AI tool can undertake the complete lifecycle of a scientific experiment at a cost of just US$15 per paper – less than the cost of a scientist’s lunch.

These are some big claims. Do they stack up? And even if they do, would an army of AI scientists churning out research papers with inhuman speed really be good news for science?

How a computer can ‘do science’

A lot of science is done in the open, and almost all scientific knowledge has been written down somewhere (or we wouldn’t have a way to “know” it). Millions of scientific papers are freely available online in repositories such as arXiv and PubMed .

LLMs trained with this data capture the language of science and its patterns. It is therefore perhaps not at all surprising that a generative LLM can produce something that looks like a good scientific paper – it has ingested many examples that it can copy.

What is less clear is whether an AI system can produce an interesting scientific paper. Crucially, good science requires novelty.

But is it interesting?

Scientists don’t want to be told about things that are already known. Rather, they want to learn new things, especially new things that are significantly different from what is already known. This requires judgement about the scope and value of a contribution.

The Sakana system tries to address interestingness in two ways. First, it “scores” new paper ideas for similarity to existing research (indexed in the Semantic Scholar repository). Anything too similar is discarded.

Second, Sakana’s system introduces a “peer review” step – using another LLM to judge the quality and novelty of the generated paper. Here again, there are plenty of examples of peer review online on sites such as openreview.net that can guide how to critique a paper. LLMs have ingested these, too.

AI may be a poor judge of AI output

Feedback is mixed on Sakana AI’s output. Some have described it as producing “ endless scientific slop ”.

Even the system’s own review of its outputs judges the papers weak at best. This is likely to improve as the technology evolves, but the question of whether automated scientific papers are valuable remains.

The ability of LLMs to judge the quality of research is also an open question. My own work (soon to be published in Research Synthesis Methods ) shows LLMs are not great at judging the risk of bias in medical research studies, though this too may improve over time.

Sakana’s system automates discoveries in computational research, which is much easier than in other types of science that require physical experiments. Sakana’s experiments are done with code, which is also structured text that LLMs can be trained to generate.

AI tools to support scientists, not replace them

AI researchers have been developing systems to support science for decades. Given the huge volumes of published research, even finding publications relevant to a specific scientific question can be challenging.

Specialised search tools make use of AI to help scientists find and synthesise existing work. These include the above-mentioned Semantic Scholar, but also newer systems such as Elicit , Research Rabbit , scite and Consensus .

Text mining tools such as PubTator dig deeper into papers to identify key points of focus, such as specific genetic mutations and diseases, and their established relationships. This is especially useful for curating and organising scientific information.

Machine learning has also been used to support the synthesis and analysis of medical evidence, in tools such as Robot Reviewer . Summaries that compare and contrast claims in papers from Scholarcy help to perform literature reviews.

All these tools aim to help scientists do their jobs more effectively, not to replace them.

AI research may exacerbate existing problems

While Sakana AI states it doesn’t see the role of human scientists diminishing, the company’s vision of “a fully AI-driven scientific ecosystem” would have major implications for science.

One concern is that, if AI-generated papers flood the scientific literature, future AI systems may be trained on AI output and undergo model collapse . This means they may become increasingly ineffectual at innovating.

However, the implications for science go well beyond impacts on AI science systems themselves.

There are already bad actors in science, including “paper mills” churning out fake papers . This problem will only get worse when a scientific paper can be produced with US$15 and a vague initial prompt.

The need to check for errors in a mountain of automatically generated research could rapidly overwhelm the capacity of actual scientists. The peer review system is arguably already broken , and dumping more research of questionable quality into the system won’t fix it.

Science is fundamentally based on trust. Scientists emphasise the integrity of the scientific process so we can be confident our understanding of the world (and now, the world’s machines) is valid and improving.

A scientific ecosystem where AI systems are key players raises fundamental questions about the meaning and value of this process, and what level of trust we should have in AI scientists. Is this the kind of scientific ecosystem we want?

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List of open questions

This page is a collection of open problems in theoretical computer science. I have not investigated all of them thoroughly, but I find them interesting. It also features a list of other lists of open problems.

Some problems are very precisely formulated, others are fuzzier. The categories are here for convenience but they are mostly random.

Some of these problems are existing conjectures, though I avoided those that everyone should know, like P vs NP . For problems which are well-known conjectures with existing descriptions that are better than what I could write, I have a dedicated category . Other problems are open problems left as future work in publications that I found interesting. Yet other problems come from my research: however I usually do not list problems that I am working on right now, because the phrasing of the problem (or my understanding of possible solutions) could change too quickly for me to keep this page in sync. Also, some of my questions on TCS.SE may not be immediately reflected here, as I first wait to see whether I get an answer.

For more information about directions for new research (featuring questions that are less precise but more related to my interests), you can look at my internship and PhD offers . If you are a student interested in working with me, not all problems on that page are a good choice: the problems in this list on which I believe I could reasonably supervise someone are marked with an (*).

If you know the answer to a problem, or if you have new information about it, I would be very interested to know! You can write me at a3nm <REMOVETHIS> @a3nm.net .

This document is likely to contains errors of various kinds, and I make no promises about its correctness. Please report any mistakes to the address above.

• Complexity of counting antichains in restricted poset classes
• Tradeoffs between computational and oracle complexity to learn monotone predicates on posets
• Complexity of finding linear extensions of a labeled poset in a regular language (*)
• Representing the result of duplicate consolidation in labeled posets
• Testing whether a set of words can be the set of linear extensions of a labeled poset
• Stable interpolation on partial orders
• Representing bounded treewidth partial orders
• Smallest posets with prescribed number of linear extensions
• Detour problem
• 3-coloring graphs of diameter 2
• FPRAS for the probability of obtaining a cyclic subgraph of a directed graph
• Simple paths of fixed modulo length on undirected graphs (*)
• The monk problem (*)
• Computing the treewidth of planar graphs
• Computing cliquewidth
• Optimal bound on the size of a grid minor
• Extracting a polynomial grid minor in PTIME
• Monadic second-order logic with cardinality predicates
• Graph reachability labellings with total orders
• Boolean dimension of planar posets
• Complexity of computing a simplicial decomposition
• Covering an undirected graph with cycles of length at least 5
• Oracle complexity of skyline queries
• Constraint classes where separability is decidable
• Open-world query answering with linear rules and transitivity assertions
• Decidable unary language with number restrictions
• Decidability of finite query answering with path-functional dependencies and two-variable guarded constraints
• Decidability of conjunctive query containment under bag semantics
• Determinacy of path queries by unions of path views
• Do tractable queries on probabilistic instances have tractable lineages? (*)
• Does bounded derivation depth imply finite controllability?
• What is the complexity of testing if a query is safe?
• Complexity of query evaluation parameterized by treewidth
• How can one strengthen lower bounds for probabilistic query evaluation on unbounded-treewidth families? (*)
• Lower bounds on lineage sizes
• Monotone dualization
• Explicit Boolean functions with supralinear circuits
• Conciseness gap between formulae and circuits
• Size bounds on smoothing structured circuit representations
• Shortest superpermutation
• Languages recognized by polynomial-size DFAs
• Context-freeness of primitive words
• Words without shuffle squares (*)
• Which regular tree languages can be recognised by a word automaton?
• Lower bounds on representations of provenance
• Complexity of multi-machine scheduling of jobs with start dates, end dates, and equal duration
• Which convex polytopes have volumes of polynomial bit-length?
• Well-known conjectures
• Other lists of open problems
• Complexity of an assignment problem with subsets
• Decidability of conjunctive query determinacy in the finite
• Steinberg's conjecture
• Feder-Vardi conjecture
• Complexity of counting linear extensions in posets of height 2
• Complexity of counting linear extensions in posets of dimension 2
• What is the connection between the fluted fragment and inversion-free queries?
• Compactness difference between probabilistic XML document formalisms
• Complexity of testing the equivalence of PrXMLcie

Complexity of counting antichains in restricted poset classes ¶

With Yael Amsterdamer and Tova Milo , we worked on the problem of learning monotone predicates on lattices via crowd queries. We used the result that it is #P-hard to count the number of antichains in a poset 1 . However, our results could be strengthened if we knew that hardness also held for distributive lattices . Is it also #P-hard to count antichains in distributive lattices?

More generally, the question is: on which classes of posets is it #P-hard to count antichains?

• TCS.SE question on distributive lattices

Tradeoffs between computational and oracle complexity to learn monotone predicates on posets ¶

Our work about learning monotone predicates on lattices via crowd queries shows that (under some formulations of the problem) it is computationally intractable to do so in a way that minimizes the oracle complexity (number of oracle queries). However, we were unable to analyse the oracle performance of non-optimal strategies which are computationally inexpensive.

Formally, the task is the following: we are given a poset ( V , < ) and we wish to learn exactly a Boolean predicate P : V ↦ { 0 , 1 } which is monotone : if P ( x ) = 1 and x < y then P ( y ) = 1 . A simple algorithm is to pick (uniformly at random) an element  x such that P ( x ) is unknown, evaluate P ( x ) with the oracle, integrate the consequences of the answer (set P ( y ) = 0 for all y < x if P ( x ) = 0 , set P ( y ) = 1 for all y > x if P ( x ) = 1 ), and repeat while there are unclassified element. Are there posets where the performance of this strategy (expected number of oracle queries) is significantly worse than the (computationally intractable) optimal strategy?

More generally, are there learning algorithms for this task which are computationally tractable and yet have near-optimal oracle complexity?

• Related TCS.SE question
• Another related TCS.SE question

Complexity of finding linear extensions of a labeled poset in a regular language (*) ¶

Our work on order-incomplete data studies labeled posets , which consist of a poset ( P , < ) and a function μ from P to some finite alphabet Σ . The label of a linear extension x 1 , … , x n of ( P , < , μ ) is the word μ ( x 1 ) ⋯ μ ( x n ) . A simple question is whether we can efficiently determine, given a labeled poset ( P , < , μ ) and a word w in Σ ∗ , whether ( P , < , μ ) has a linear extension of label w . Our work shows that this problem is hard even for comparatively simple  P , and shows classes of labeled posets where it is tractable. It also studies a generalization of this question where you do not consider just the free monoid Σ ∗ on Σ , but an arbitrary monoid structure: given a monoid element w and a labeled poset, we ask whether there is a linear extension whose label evaluates to w according to the monoid law.

Of course, another variant of this problem is to consider a language L on Σ , for instance a regular language, and ask whether the labeled poset has a linear extension whose label is in L . The more general question is: for which regular languages is this class tractable? Could one show a dichotomy result separating tractable and intractable languages?

For instance, with the alphabet Σ = { a , b } and language L = ( a b ) ∗ , I do not know whether it is tractable, given an input poset ( P , < , μ ) , to test whether it has a linear extension where we alternate between elements labeled a and elements labeled b .

• Our paper about the problem, which settles various special cases
• Page keeping track of the remaining open problems from the paper
• TCS.SE question about the case where the language follows the law of a finite group
• TCS.SE question about the variant of finding the lexicographically minimal topological sort
• TCS.SE question about hardness of a related problem
• TCS.SE question about hardness of a related problem on restricted poset classes

A related question is to characterize the complexity of enumerating linear extensions of labeled posets: the problem can be done in constant amortized delay for classical posets 3 , but I am not aware of analogous results for labeled posets.

• TCS.SE question about this

Representing the result of duplicate consolidation in labeled posets ¶

With M. Lamine Ba , Daniel Deutch and Pierre Senellart , we worked on how to represent and query order-incomplete data. In this context, we studied labeled posets (defined as above) and study the question of how to consolidate duplicates in a labeled poset. By this, we mean that we want to compute a labeled poset where the element labels are unique (all elements with the same label are collapsed to the same element), and the remaining order relations between the collapsed elements are sensible.

However, if you see a labeled poset as a way to represent a set of possible orders (its linear extensions), and if you want the duplicate removal operation to act consistently when looking at each linear extension (i.e., the linear extensions of the duplicate consolidation should be the result of removing duplicates in the linear extensions of the labeled posets), then it is not clear at all how to proceed. In fact, the result of duplicate consolidation may even not be representable as a labeled poset.

Is there a formalism that can represent the result of duplicate consolidation on labeled posets?

Testing whether a set of words can be the set of linear extensions of a labeled poset ¶

Define labeled posets as in the previous section. Consider a sequence S of words given as input. A labeled poset ( P , < , μ ) represents S if S is exactly the set of labels that can be achieved by the linear extensions of the poset. Of course, a sequence S cannot be thus represented unless all its sequences are built using the same multiset of elements, which should be the image of μ (seen as a multiset). However, if S respects this condition, it does not seem easy to determine whether it can be represented or not.

What is the complexity of determining, given a set of sequences, whether it can be represented by a labeled poset in this sense?

Stable interpolation on partial orders ¶

In our work with Yael Amsterdamer , Tova Milo , and Pierre Senellart , we study an interpolation scheme on partial orders, defined as the center of mass of the convex polytope defined by the order constraints. As it turns out, however, the scheme is not stable : if we fix some variables to their interpolation result, the interpolation of other variables may change.

Is there a principled stable interpolation scheme on posets? Is it unique?

• More general TCS.SE question

Representing bounded treewidth partial orders ¶

In our work with Yael Amsterdamer , Tova Milo , and Pierre Senellart , we consider partial orders whose Hasse diagram (or its reverse) is a directed tree. We do not know whether our study would extend to partial orders whose Hasse diagram has bounded treewidth.

Is there a structure on the set of linear extensions of a poset whose Hasse diagram has bounded treewidth? Alternatively, is there a structure on the convex polytope defined by such order constraints?

• Related paper which shows that it is PTIME to count the number of linear extensions of posets whose Hasse diagram has bounded treewidth.

A related question: are there languages for which constrained topological sorting is tractable on partial orders whose Hasse diagram is a tree, or has bounded treewidth, but is hard on arbitrary DAGs?

Smallest posets with prescribed number of linear extensions ¶

For all n ∈ N , what is the minimal number of elements of a poset with exactly n linear extensions , if one exists? What is the asymptotic growth of this function?

• Math.SE question

The analogous question for antichains has been studied 4 , with posets of size logarithmic in the desired number of antichains. However, the argument is much simpler, because the posets can be easily constructed from smaller posets. By contrast, the number of linear extensions of a poset seems hard to determine from elementary "constituent parts".

Detour problem ¶

Given a directed graph G , a source vertex s , and a sink vertex t reachable from s , we want to know if there is a simple directed path from s to t whose length is greater than that of the shortest path from s to t . Is this problem in polynomial time?

• Last seen open: 2023 5

A seemingly related question is that of simple paths on DAGs with backward edges. Consider an input DAG G , two vertices s and t , and additional back edges such that whenever ( u , v ) is an additional edge then u is reachable from v in  G . Is it NP-hard to determine whether there is a simple path from s to t that uses at least one additional edge?

• TCS.SE question

3-coloring graphs of diameter 2 ¶

An undirected graph has diameter 2 if, for every pair of vertices u ≠ v , there is a path of length at most 2 connecting u and v (i.e., with at most one intermediate vertex). A 3-coloring of a graph is a function mapping each vertex to a value in { 1 , 2 , 3 } such that no two adjacent vertices are mapped to the same color.

Given a graph of diameter 2, can we decide in polynomial time whether it admits a 3-coloring?

• Last seen open: 2024 6

FPRAS for the probability of obtaining a cyclic subgraph of a directed graph ¶

We are given a directed graph G whose edges are annotated with independent probabilities of existence, and we want to estimate the probability of obtaining a subgraph of G which contains a directed cycle. Is there an FPRAS for this task?

• CStheory question (2023)
• Paper leaving the problem open (to appear in 2024)

Simple paths of fixed modulo length on undirected graphs (*) ¶

Given an undirected graph and two nodes, can one decide in polynomial time whether there is a simple path of length 0 modulo 3 between the two nodes?

• Last seen open: 2022 7 .

The problem without the "simple" requirement is clearly in PTIME, and the same problem on a directed graph is NP-hard by a reduction from the 2 disjoint paths problem. The question is also open for paths of length p modulo q for other values of p and q . It can be determined in PTIME if all simple paths between two vertices of an undirected graphs are of length p modulo q, solving the problem for q = 2 8 .

Up to subdividing each edge by 2 and connecting the source and target nodes by an edge, we can reduce to the problem of deciding if an undirected graph has a simple cycle of length 2 p + 1 mod 2 q . This question is also open: a related comment is at the end of these slides (2015). A sufficient condition for tractability was given in 2004 9 , but it does not cover the right cases, so the problem remains open.

I have written (in 2023) a more detailed writeup on the related work around this problem.

The monk problem (*) ¶

The so-called monk problem 10 is a pursuit-evasion game played on a directed graph . A strategy for k pursuers is a sequence s 1 , … , s n of subsets of k vertices. A strategy is winning if, for every (non-simple) walk v 1 , … , v n in the graph, there is i such that v i ∈ s i . Intuitively, the evader is walking on the graph (it has to move at each turn by following exactly one edge) and must avoid the k vertices that the pursuers examine at each time step.

The evasion number of a digraph G is the smallest k for which the pursuers have a winning strategy. What is the computational complexity, given an input digraph, of computing its evasion number? This relates to the question of whether graphs with evasion number ≥ k can be somehow characterised, similarly to the links between treewidth and pursuit-evasion via havens . It also relates to the question of how the maximal length of a strategy can be bounded as a function of the graph size and of k .

• Bruteforce implementation
• Paper which characterizes the undirected graphs with evasion number k = 1 (they are the unions of lobster graphs , and can be recognized in linear time), and determines explicit strategies for them. In this paper the pursuer is called a prince and the evader is called a princess . See also this Reddit discussion , where the pursuer is a vampire hunter and the evader is a vampire .
• Catching a mouse on a tree , where the pursuers are called cats and the evader mouse ;
• Hunting rabbits on the hypercube , which follows the hunter/rabbit terminology.

Computing the treewidth of planar graphs ¶

Treewidth measures how much an undirected graph is close to a tree. It is known that, for any fixed k ∈ N , we can check in linear time in an input graph G whether its treewidth is ≤ k ; but that, when both k and G are given as input, it is NP-hard to determine whether G has treewidth ≤ k .

Is this last statement still true if G is planar, or can the treewidth of a planar graph G be computed in PTIME?

Computing cliquewidth ¶

The parameterized cliquewidth computation problem for k ∈ N asks, given an input graph G , whether G has cliquewidth ≤ k . Is this problem in PTIME for any fixed k ? Is there k ∈ N such that the problem is NP-hard?

Membership in PTIME was recently shown 17 for k ≤ 3 , but the problem is open for larger k . In particular, we do not know whether the problem is in FPT . Membership in FPT is known for some restricted classes of graphs of unbounded cliquewidth 18 , and membership in cubic FPT is known for the related parameter of rankwidth 19 .

• Last seen open: 2012 17 .

Optimal bound on the size of a grid minor ¶

The grid minor theorem 20 of Robertson and Seymour shows that, if a family of graphs has unbounded treewidth , then one can find arbitrary large grid graphs as minors of the family. Specifically, the result can be stated as follows 21 : there exists a function f : N > 0 → N > 0 such that, for every g ∈ N > 0 , every graph of treewidth ≥ g has the ( g × g ) -grid as a minor.

The best known upper bound 21 on  f is ~ O ( g 19 ) , where the ~ O notation neglects polylogarithmic factors. The best known lower bound 22 is Ω ( g 2 log g ) .

What is the correct bound on the function f ?

• Last seen open: 2016 21 . See 21 for discussion of conjectured bounds.

Extracting a polynomial grid minor in PTIME ¶

Continuing on the grid minor theorem from the previous entry, the following result is known 23 : there is c ∈ N such that for any n ∈ N , for any graph G of treewidth ≥ n c , one can find the n × n grid as a minor of  G . This work shows how the minor can be found in randomized polynomial time .

Is it possible to extract the minor in deterministic PTIME?

• Last seen open: 2015 24 .

Monadic second-order logic with cardinality predicates ¶

We extend monadic second-order logic (MSO) over graphs with constructs to check the equality of the cardinalities of second-order variables, and check that their cardinalities are in fixed recursive sets . We fix a formula Φ in this logic and a treewidth bound k ∈ N . Is it PTIME in an input graph G of treewidth ≤ k to check whether it satisfies Φ ?

Courcelle's theorem states that this is true (and in linear time) for normal MSO without the extension.

• The question on Open Problem Garden

Graph reachability labellings with total orders ¶

A labeling of a directed acyclic graph (DAG) G = ( V , E ) is a function μ from V to some set Σ of labels such that the labels of a pair of vertices suffice to test reachability . Formally, there is a decoding function f : Σ 2 → { 0 , 1 } independent of G such that for any two vertices u , v ∈ V , we have f ( μ ( u ) , μ ( v ) ) = 1 iff v is reachable from u in G .

I am interested in labeling schemes where Σ is N d for a certain d , and where for simplicity we assume that μ cannot use the same number twice: there are no u ≠ v in V such that, letting ℓ = μ ( u ) and ℓ ′ = μ ( v ) , we have ℓ i = ℓ ′ j for some 1 ≤ i < j ≤ d . Further, the decoding function f can only use the labels to do comparisons on their components, i.e., f , when applied on ( ℓ , ℓ ′ ) can only see whether ℓ i < ℓ ′ j for all 1 ≤ i , j ≤ d . Given d ∈ N and a choice of decoding function f , the labelable graphs of f are those for which there is a reachability labeling scheme for f .

These definitions generalize several known notions:

The case d = 1 is uninteresting: there is only a single possible scheme f , and the labelable graphs are the directed path graphs .

For d = 2 , considering the decoding function f ( ℓ , ℓ ′ ) that checks whether ℓ 2 < ℓ ′ 1 , the labelable graphs are those that represent interval orders

For d = 2 , considering the decoding function f ( ℓ , ℓ ′ ) which is true iff ℓ 1 < ℓ ′ 1 and ℓ 2 < ℓ ′ 2 , the labelable graphs are those that represent posets with order dimension at most two. More generally, for arbitrary d ∈ N , for the function that takes the AND of the pointwise comparability relations, the labelable graphs are those that represent a partial order with dimension ≤ d .

For other values of d and decoding functions, how can we characterize the labelable graphs? In particular, for a given value of d , are some decoding functions more expressive than others? (For d = 2 and the two decoding functions that I presented, interval orders and orders of dimension ≤ 2 are incomparable.) Further, is there d ∈ N and some decoding function such that any graph has a reachability labeling with N d ? (This sounds extremely unlikely but I'm not sure of how to prove it.)

• Preliminary notes about these problems
• It appears that the notion of labeling schemes with decoding function presented here, up to some minor differences, has been introduced in this paper 31 (see conclusion) under the name local presentation . In their terminology, a local presentation of a DAG is a function mapping each vertex to a d -tuple of integers, with the decoding function being a Boolean function of equalities and inequalities on the tuple components: this is exactly the definition above except that the same number can be used multiple times and we can test for equality. The notion does not seem to have been studied again since that paper, though there have been studies of the related notion of Boolean dimension: this is the case where we can only do comparisons between ℓ i and ℓ ′ i , i.e., between the same components of the labels. In particular I didn't find an example of a poset family where the size d of local presentations was unbounded.

Boolean dimension of planar posets ¶

Let G = ( V , E ) be a directed acyclic graph (DAG). A Boolean realizer of G is intuitively a way to label each vertex of G with integers, such that reachability in G can be determined only by looking at some Boolean function over pairwise comparisons of the vertex labels. Formally, a Boolean realizer of G of dimension d ∈ N consists of a Boolean function ϕ on d variables, and of d labellings ℓ 1 , … , ℓ d , each of which is an injective function from V to N : we require that for any two vertices u , v ∈ V , letting x i for all 1 ≤ i ≤ d be 1 if ℓ i ( u ) < ℓ i ( v ) and 0 otherwise, we have ϕ ( x 1 , … , x d ) = 1 iff v is reachable from u in G . The Boolean dimension of G is then the smallest d for which G has a Boolean realizer of dimension d .

Is the Boolean dimension of planar DAGs bounded? In other words, is there a constant k ∈ N such that, whenever G is planar (i.e., it can be drawn in a way such that no two edges cross), then the dimension of G is no greater than k ?

• Posed in: 1989 (cited in 32 )
• Last seen open:  2018 32

Complexity of computing a simplicial decomposition ¶

A simplicial decomposition of a graph G is a tree decomposition such that, for any two adjacent bags b and b ′ whose set of vertices is respectively X and X ′ , the subgraph induced by G on X ∩ X ′ is a clique. The width of the decomposition is the size of the largest bag minus one, as usual for treewidth. The simplicial width of G is the smallest possible width of a simplicial decomposition. What is the complexity, given a graph G , of computing its simplicial width and a simplicial decomposition? One can ask the question when allowing arbitrary G , or when assuming that the simplicial width of the input graph is bounded by a constant.

Note that there are known results 33 on the complexity of computing a clique minimal separator decomposition, i.e., a simplicial decomposition where we minimize the size of the cliques, not of the bags.

• Paper of mine which uses simplicial decompositions.

Covering an undirected graph with cycles of length at least 5 ¶

What is the complexity of determining if an input undirected graph can be covered by cycles, each of which have length at least 5? The problem is known to be PTIME for a length constraint of "at least 3" or "at least 4", and NP-hard for a length constraint of "at least k " for all k ≥ 6 .

Databases and logic ¶

Oracle complexity of skyline queries ¶.

Consider a set of d -dimensional vectors V = v 1 , … , v n of numbers (or indeed any totally ordered set). Let us assume for simplicity that all the v i l are distinct for 1 ≤ i ≤ n and 1 ≤ l ≤ d . In this context, we say that v i dominates v j if v i l ≥ v j l for all 1 ≤ l ≤ d . The skyline (or Pareto frontier ) of V is the set of maximal vectors for the domination relation.

Assume that the only way you can access the vectors of V is by atomic comparisons, i.e., you can evaluate whether v i l < v j m for any 1 ≤ i , j ≤ n , 1 ≤ l , m ≤ d . What are bounds on the minimal number of comparisons required to determine the skyline? Such bounds can be stated as a function of k and n , or as a function of the output size (the actual skyline).

Groz and Milo 11 have studied this problem when the comparisons are additionally noisy, but good bounds for d > 3 are not yet known, even without noise.

Constraint classes where separability is decidable ¶

Consider a set Σ of tuple-generating dependencies (TGDs) and a set Φ of equality-generating dependencies (EGDs). We say that a Boolean conjunctive query (CQ) Q is entailed by a relational database instance I and by Σ ∧ Φ if, for every superinstance I ′ ⊇ I such that I ′ satisfies Σ ∧ Φ , it is the case that I ′ satisfies Q . Intuitively, Q is implied by the instance I and the constraints Σ ∧ Φ under open-world semantics : Q is true on all superinstances of I that satisfy the constraints Σ ∧ Φ .

We call Σ and Φ separable if, for any Boolean CQ Q and instance I that satisfies Φ , the following equivalence holds: Q is entailed by I and Σ ∧ Φ iff Q is entailed by I and Σ . In other words, the equality-generating dependencies Φ can be checked separately on  I , and have no impact afterwards in terms of entailment.

For general TGDs and EGDs, the problem is undecidable 12 , but this is not so surprising as reasoning with TGDs by themselves is also undecidable if arbitrary TGDs are allowed. Are there less expressive languages for which separability is decidable? One could think, e.g., of inclusion dependencies and functional dependencies , maybe with some restrictions.

Open-world query answering with linear rules and transitivity assertions ¶

A linear rule is a tuple-generating dependency (TGD) with exactly one atom in the body and one atom in the head. A transitivity assertion on an arity-two relation R is a TGD of the form ∀ x y z   R ( x , y ) ∧ R ( y , z ) ⇒ R ( x , z ) .

It is decidable 25 whether an instance I and constraints Σ of linear rules and transitivity assertions entail a CQ Q , in the sense of the previous problem, but under some restrictions (all relations have arity at most two, or Q consists of a single atom, or an additional condition holds). Does decidability hold in the general case of arbitrary CQ and arbitrary arity signatures for linear rules and transitivity assertions?

Decidable unary language with number restrictions ¶

With Michael Benedikt we introduced a language formed of expressive constraints on an arity-two signature (including number restrictions, namely counting quantifiers ) and tuple-generating dependencies on arbitrary arity predicates, also supporting functional dependencies of a restricted kind on such predicates. We showed that it was decidable to determine (in the sense above) whether a query is entailed by an instance and such constraints, which we call the open-world query answering (OWQA) problem.

This raises the question of whether a more expressive and more uniform such language could be designed. It should also have decidable entailment, and should also feature (1) arbitrary arity constraints, (2) number restrictions such as functional dependencies, and (3) expressive logical operators such as disjunction. Can such a language be designed? Relevant results include the following (beyond the ones shown in the paper mentioned above):

• OWQA is decidable for the two-variable guarded fragment of first-order logic with counting quantifiers 26 . This covers (2) and (3).
• OWQA is decidable for the guarded fragment of first-order logic 27 : this covers (1) and (3).
• OWQA is decidable with functional dependencies and unary functional dependencies, thanks to the fact that they satisfy the non-conflicting condition 28 . The same holds for other classes of tuple-generating dependencies for which OWQA is decidable (e.g., guarded tuple dependencies) and functional dependencies. This covers (1) and (2).
• OWQA is not decidable for inclusion dependencies and functional dependencies in general, because their implication problem is undecidable 29 , and it reduces 30 to OWQA. This means we cannot have (1) and (2) without restrictions.

A general idea would be to design a language that generalizes frontier-one TGDs to have disjunction and some kind of "non-conflicting" counting quantification, and establish decidability.

Following this paper , another natural direction would be to study finite model reasoning for such a language. However, one should first show the decidability of the finite implication problem for it: decide whether a set of constraints of the language implies other constraints. Yet, as far as I know, the only decidability result for finite implication on an arbitrary-arity language that features number restrictions only covers 40 unary inclusion dependencies and functional dependencies . Can finite implication be decided for a more expressive language of this form? E.g., in the spirit of existing works 41 but for arbitrary arity constraints.

Decidability of finite query answering with path-functional dependencies and two-variable guarded constraints ¶

This question uses the definition of OWQA from the previous question. It was recently shown 42 that the finite satisfiability problem is decidable for the two-variable guarded fragment of first-order logic with counting quantifiers (GC²) to which one adds path-functional dependencies. Is the same true of the finite OWQA problem? This is already known if there are no path dependencies 26 .

If this is true, it would imply an independent proof of the result of this paper when assuming that all functional dependencies are unary. Indeed, unary inclusion dependencies and functional dependencies on arbitrary signatures can clearly be equivalently translated to GC² plus path functional dependencies (with paths of length 2). To re-prove this result for arbitrary functional dependencies, one would need some generalization of path functional dependencies (to capture the image of this translation).

Decidability of conjunctive query containment under bag semantics ¶

Is conjunctive query containment under bag semantics decidable, and what is its complexity?

• Slides (2013) that define the problem.

Determinacy of path queries by unions of path views ¶

For k ∈ N , the path query q k of length k on a directed graph G = ( V , E ) returns the set of pairs of nodes ( u , v ) ∈ V 2 such that there is a path of length k from  u to  v . A union of path queries q S is defined by a (possibly infinite) set S of integers and returns the sets of pairs of nodes ( u , v ) such that there is a path from u to v whose length is in S .

A set of union of path queries Q = q S 1 , … , q S n determines a path query q k if, for all finite graphs G and G ′ , if q S i ( G ) = q S i ( G ′ ) for all 1 ≤ i ≤ n , then q k ( G ) = q k ( G ′ ) . Under mild assumptions on the representation of infinite sets in union of path queries, the determinacy problem was shown 44 to be decidable but only for path queries q k where k is larger than some function of Q . Is it decidable to determine whether a path query is determined by a set of union of path queries, without this restriction?

Another question is whether this result extends to more general query languages. For instance, is it decidable to determine whether a union of path queries is determined by a set of union of path queries?

A natural further generalization of this problem is going from paths of a fixed length to paths labeled by some language, when edges are labeled by letters of some alphabet. Formally, we define a regular path query q L as a query on edge-labeled graphs that returns the pairs of vertices connected by a path in L , where L is a regular language over the alphabet of edge labels. In this context, however, it was shown that it was undecidable whether a regular path query was determined by a set of regular path queries 45 , and it is even undecidable whether using only finite regular languages 46 (or, equivalently, union of labeled path queries , i.e., unions of queries returning all pairs of vertices separated by a path labeled by some finite word). So with these generalisations of the above problem being undecidable, it is not clear whether we should expect decidability for (unlabeled) path queries, or unions thereof.

Thanks to Nadime Francis and to Bartosz Bednarczyk for helping me to prepare this entry.

Do tractable queries on probabilistic instances have tractable lineages? (*) ¶

A tuple-independent database (TID) is a probabilistic database consisting of a relational database I where each tuple is given a probability in [ 0 , 1 ] . The semantics is a probability distribution on subsets of I (the possible worlds ), obtained by considering that each tuple is either kept or removed with the indicated probability, independently across tuples.

A Boolean union of conjunctive queries (UCQ) is a disjunction of conjunctive queries with no free variables . The probability evaluation problem for a fixed Boolean UCQ q asks, given a TID I , what is the probability that I satisfies q , meaning, what is the total probability mass of possible worlds of I that satisfy q . A dichotomy result is known 47 : Boolean UCQs are partitioned between those for which the probability evaluation problem can be solved in polynomial time, and those where it is #P-hard .

The lineage of a Boolean query q on a TID instance I is a Boolean formula whose variables are the facts of I , such that a valuation makes the circuit evaluate to true iff the corresponding possible world (defined by keeping exactly the facts set to true) satisfies q . One way to show that a Boolean UCQ is tractable is to show that, on any instance, one can represent its lineage in a form that allows for tractable probability evaluation.

A d-DNNF ¬ is a Boolean circuit (with AND, OR, NOT gates, and input gates) such that every AND gate is on disjoint set of variables (meaning, there is no input gate reachable from two distinct children of an AND gate), and every OR gate is exclusive (meaning, there is no valuation of the input gates that makes two distinct children of an OR gate evaluate to true). A Boolean UCQ has polynomial-size d-DNNF ¬ if there is a constant c ∈ N such that, for any TID instance I , there is a d-DNNF ¬ of size O ( | I | c ) that expresses the lineage of q on I .

It is known 48 that many Boolean UCQs for which probabilistic query evaluation is in PTIME have polynomial-size d-DNNF ¬ , but the converse is open. Is there a Boolean UCQ for which probabilistic query evaluation is in PTIME, but that has no polynomial-size d-DNNF ¬ ? In particular, is this the case of the conjectured 48 counterexample Q 9 ? If this can be shown, is it possible to design a generalization of d-DNNF ¬ that still enjoys probabilistic query evaluation, and is such that any Boolean UCQ with PTIME probabilistic query evaluation has a polynomial-size lineage in this generalization?

Update: the most recent work in this area is this paper by Mikaël Monet

Does bounded derivation depth imply finite controllability? ¶

We talk of a Boolean conjunctive query Q being entailed by an instance I and set Σ of tuple-generating dependencies (TGDs) if for any instance I ′ ⊇ I such that I ′ ⊨ Σ , we have I ′ ⊨ Q .

The set Σ of tuple-generating dependencies (TGDs) has bounded derivation depth if, for any conjunctive query Q , there exists a union of conjunctive queries Q ′ such that, for any relational instance I , the following equivalence holds: Q is entailed by I and Σ iff I ⊨ Q ′ .

The set Σ of TGDs is finitely controllable iff for any instance I and Boolean conjunctive query Q , the following equivalence holds: Q is entailed by I and Σ iff Q is entailed by I and Σ over finite models (impose that I ′ is finite in the definition above).

Is it the case that if a set of TGDs has bounded derivation depth then it is finitely controllable? In the work where this conjecture was posed 49 , it was solved for signatures of arity two, but the general question remains open.

What is the complexity of testing if a query is safe? ¶

This question refers to the dichotomy 47 on the Boolean UCQs for which the probability evaluation problem is in PTIME: see this question for background. The queries which are tractable according to this dichotomy are safe .

What is the complexity, given a Boolean UCQ, to determine whether it is safe?

The best known algorithm for this is super-exponential 15 .

• Last seen open:  2011 15

Complexity of query evaluation parameterized by treewidth ¶

The query evaluation problem asks, given a Boolean conjunctive query Q and a relational database I , whether Q holds on I . The treewidth of  I is the treewidth of its Gaifman graph , and the treewidth of Q is that of its canonical instance (i.e., we just see the query as a database on its variables). What is the parameterized complexity of the query evaluation problem when parameterized by the treewidth of  I and of  Q ? (In other words, the parameter of the problem is an upper bound on the treewidth of both I and  Q .)

• CStheory question where the problem is phrased in terms of graph homomorphisms (query evaluation can be understood as deciding the existence of a homomorphism between labeled hypergraphs). Also includes pointers to related work.

How can one strengthen lower bounds for probabilistic query evaluation on unbounded-treewidth families? (*) ¶

In this paper with Pierre Bourhis and Pierre Senellart , we showed (Theorem 4.2) that there is a query for which the probabilistic query evaluation problem (see this question for the definition) is intractable on any unbounded-treewidth instance family. However, the lower bound of this result has some limitations, and I do not know whether they can be lifted:

• Does the result generalize to arbitrary arity signatures rather than arity-2 signatures?
• Can the query be in a weaker language than MSO? For instance, can it be a union of conjunctive queries with inequalities ( UCQ ≠ )?
• Does the result hold even if we are not completely free to choose the probability valuation of the input instance?
• Is it possible to use PTIME reductions rather than RP reductions? This is asked separately as this question .

Lower bounds on lineage sizes ¶

In the same paper as in the previous question, we showed (in Lemma 8.2) that, for any graph signature, there is a UCQ with inequalities Q such that, given any instance I , the width of any OBDD representing the lineage of  Q on  I (see this question for the definition) is bounded by an exponential function of the treewidth of  I : specifically, there is a constant c ∈ N > 0 such that it is in Ω ( 2 ( width ( I ) ) 1 / c ) .

Can the same result be shown for other lineage representations? In particular, can it be shown for d-DNNFs?

Update: our ICDT'19 paper with Mikaël Monet and Pierre Senellart shows a similar lower bound for the class of d-SDNNF (structured d-DNNF). The question of showing a similar bound for d-DNNF is very challenging and relates to the open problem of separating DNFs in general and d-DNNFs.

Boolean functions and circuits ¶

Monotone dualization ¶.

The prime CNF of a monotone Boolean function over variables x 1 , … , x n is the (unique up to order) expression of the function as a conjunction of disjunctions of the x i from which no variable occurrence can be removed. The dual of a monotone Boolean function f is the monotone Boolean function mapping x 1 , … , x n to ¬ f ( ¬ x 1 , … , ¬ x n ) . By De Morgan's laws , a Boolean expression for the dual can be obtained by replacing ∧ 's by ∨ 's and vice-versa in the prime CNF of f .

The Dual problem asks, given two prime CNFs, whether the functions defined by these CNFs are dual of one another. It is known to be in quasipolynomial time 16 . Is the Dual problem in PTIME?

Explicit Boolean functions with supralinear circuits ¶

Shannon proved in 1949 with a counting argument that most Boolean functions cannot be represented by a circuit of linear size. However, we do not know yet of any explicit Boolean function for which no linear size circuit exists. Can we construct such a function?

• TCS.SE question about the lowest classes for which a supralinear bound is known

Conciseness gap between formulae and circuits ¶

Boolean functions can be represented as circuits or as formulae. Circuits seem much more concise, because they can reuse common subexpressions. Yet the best conciseness gap known is the following: there are Boolean functions that can be represented by linear circuits but for which any formula representation has size at least n 3 − o ( 1 ) (over circuits with AND, OR, and NOT). Can we do better?

Size bounds on smoothing structured circuit representations ¶

A Boolean circuit is structured if there is a fixed full binary tree whose leaves are labeled by the variables (the vtree ) and a mapping from the gates of the circuit to the nodes of the tree such that every variable is mapped to the leaf corresponding to itself and the inputs to every gate g are mapped to descendants of the node to which g is mapped. A Boolean circuit is smooth if, intuitively, no variable is omitted, i.e., whenever we take the disjunction of two gates then the set of variables reachable from each gate is the same.

Given a Boolean structured circuit, what is the complexity of computing an equivalent circuit which is structured but still smooth? What about the same question while preserving other desirable circuit properties such as being deterministic?

• Paper with complete definitions and a partial result (Proposition 7.1)

A circuit is decomposable if the inputs to every AND-gate depend on pairwise disjoint sets of variables. What can be said about the same question for smoothing decomposable circuits? There is a partial result (applying only to a certain class of "smoothing-gate algorithms") as Theorem 5.2 in the paper above.

Formal languages ¶

Shortest superpermutation ¶.

An n -superpermutation is a word w over { 1 , … , n } such that each permutation of { 1 , … , n } occurs as a subsequence of w . What is the length of the shortest n -superpermutations as a function of n ?

• Wikipedia page
• Quanta Magazine article from 2018
• MO.SE question

Languages recognized by polynomial-size DFAs ¶

Which languages can be recognized by a (not necessarily uniform ) family of deterministic finite automata of polynomial size?

Context-freeness of primitive words ¶

A primitive word is a word that cannot be represented as a power of another word. Is it true that, on any alphabet with more than one letter, the set of all primitive words is not context-free?

• There is a book about the question (not available online): P. Domosi, M. Ito, Context-Free Languages and Primitive Words

Words without shuffle squares (*) ¶

Fix an alphabet Σ . We say that a word w ∈ Σ ∗ is the shuffle of two words u , v ∈ Σ ∗ if we can obtain w by interleaving u and v . A word w ∈ Σ ∗ is a shuffle square if there is a word u ∈ Σ ∗ such that we can obtain w as the shuffle of u and u . (Note that this implies that, for each letter a ∈ Σ , there is an even number of occurrences of a in w . While the number of occurrences of each letter in u are uniquely defined from w , the order of the letters is not.) We say that a word is shuffle-square-free if it contains no substring which is a shuffle-square.

If the alphabet Σ has at least 6 letters then it is known that there exist infinitely many shuffle-square-free words 50 , following an earlier result 51 on alphabet size 7 . If the alphabet Σ has 3 letters or less, then it is known 52 that such words do not exist: the longest such words on Σ = { a , b , c } are abcacbacabc, acbabcabacb, bacbcabcbac, bcabacbabca, cabcbacbcab, cbacabcacba, of length 11 each. (I'm adding them to this entry to ensure that people interested in this computation can easily find the page. ;)) The question is open for alphabets of size 4 and 5.

Are there infinitely many shuffle-square-free words on an alphabet of size 4?

• Source code repository which we used to bruteforce the computation of large shuffle-square-free words using a SAT solver. Some documentation is provided as a README. This is joint work with Charles Paperman .

Which regular tree languages can be recognised by a word automaton? ¶

Given a tree alphabet Σ , we define the alphabet ¯ Σ to consist of { a ∣ a ∈ Σ } ∪ { ¯ a ∣ a ∈ Σ } . Given an unranked tree T on a tree alphabet Σ , the XML representation of T is the word on ¯ Σ recursively defined as follows: the coding of a leaf labeled a ∈ Σ is a ¯ a , and the coding of an internal node labeled a ∈ Σ with children n 1 , … , n k is a c 1 ⋯ c k ¯ a where each c i is the coding of n i .

Given a tree automaton A on unranked trees on Σ , it defines a so-called regular tree language L ( A ) , and we denote by X M L ( L ( A ) ) the word language on ¯ Σ of the XML codings of trees of L ( A ) . Of course, for all regular tree languages except finite ones, X M L ( L ( A ) ) is not regular as a word language, because a word automaton cannot check if the opening and closing tags (i.e., the a 's and ¯ a 's) are properly nested. The question is intuitively to understand the regular tree languages for which matching the opening and closing tags is the only difficulty.

Formally, we say that a word automaton A weakly recognises a tree language L if, given a word w on ¯ Σ which is the XML representation of some tree T , then A accepts w iff T ∈ L . (The behavior of A on words of ¯ Σ that do not represent any tree is not specified.)

Given a tree automaton A , is it decidable to determine if there exists a word automaton that weakly recognizes the language X M L ( L ( A ) ) ?

The problem, in the specific case of DTDs (a special case of tree automata), has been shown 53 to be equivalent to a variant of the word problem for groups, whose decidability status is open. The status of the general problem is also open.

Thanks to Bartosz Bednarczyk for pointing out this problem to me, and to Charles Paperman for the problem phrasing used here.

Miscellaneous ¶

Lower bounds on representations of provenance ¶.

The Why-provenance 54 of a Boolean query q in the positive relational algebra on a relational instance I is a Boolean function ϕ defined on the facts of I such that, for any valuation ν mapping each fact of I to true or false, ν ( ϕ ) is true iff { F ∈ I ∣ ν ( F )  is true } satisfies q .

It is known 54 that, for any such fixed query q , its Why-provenance on I can be represented as a Boolean formula of polynomial size in the instance I . Are there instance families with known lower bounds on the representation of Why-provenance? In particular, is there a query q and family of relational instances I 1 , … , I n , … , such that, letting ϕ i for all i be the Why-provenance of q on I n , the size of ϕ i is superlinear in I i , namely, there is no constant K such that, for all i , the provenance ϕ i can be written as a Boolean formula of size less than K ⋅ | I | , where | I | is the number of facts of I .

The question generalizes to other representations of provenance, such as provenance circuits 55 , or to provenance expressed in different provenance semirings 54 , such as the universal semiring N [ X ] of polynomials in X (standing for the facts of I ).

Complexity of multi-machine scheduling of jobs with start dates, end dates, and equal duration ¶

We have a certain number m of machines, and a number n of jobs. All jobs have the same duration (an integer p ), and each job has a minimum start date and a maximal end date , both of which are integers. The scheduling problem asks whether there is a way to schedule all n jobs on the m machines. We can phrase it in two variants: the decision variant simply asks whether it is possible, and the computation variant asks us to compute a possible schedule, i.e., a partition of the n jobs into m sequences such that each machine can perform its sequence of m jobs in a way that respects the start date and end dates of all jobs, and the job duration. The problem can equivalently be phrased with jobs of unit duration and start and end dates which are rationals.

Somewhat surprisingly (to me at least), this problem can be solved in PTIME. The best known algorithm 60 (which additionally optimizes an additional criterion) runs in time O ( m i n ( 1 , p m ) n 2 ) . What is the most efficient algorithm for this problem?

For the case m = 1 , a more efficient algorithm is known 61 , which runs in O ( n log n ) . In this setting, there is a clear lower bound of Ω ( n log n ) for the computation problem, as the scheduling problem for jobs with disjoint intervals amounts to sorting their bounds; but for the decision problem, this is unclear.

Thanks to the judges of the 2017 ACM-ICPC World Finals for bringing this problem to my attention (see Problem H, "Scenery").

Which convex polytopes have volumes of polynomial bit-length? ¶

In this question, all numbers are represented as rationals. Consider a convex polytope described as an intersection of half-spaces , each of which is described as inequalities between a linear function of the coordinates and a constant (e.g., x 1 + 7 42 x 2 ≤ 3 ). We assume that the polytope is bounded, i.e., it is not infinite. Given such a representation, we wish to compute the volume of the polytope. It turns out 62 that this cannot be done in polynomial time (or even in nondeterministic PTIME) because the volume is not always of polynomial length in the input description. Hence the question: For which classes of polytopes is the volume always of polynomial length in the input?

Well-known conjectures ¶

• The 1/3-2/3 conjecture : In every non-totally-ordered poset P , there are x and y such that x < y in at least 1/3 and at most 2/3 of the linear extensions of P .
• The removable pair conjecture : Can you always remove two elements from a poset of ≥ 3 elements such the order dimension drops by at most 1?
• The union-closed sets conjecture : calling a family of sets union-closed if the union of any sets in the family remains in the family, is it true that any union-closed finite family of finite sets must have an element occurring in at least half the sets of the family? (except the family containing just the empty set)
• The reconstruction conjecture : Given a graph G with n vertices, its deck is the multiset of the n subgraphs obtained, for each vertex, by deleting this vertex and its incident edges. For n ≥ 3 , if two graphs have the same deck (up to isomorphism), are they necessarily isomorphic?
• What is the complexity of matrix multiplication ?
• Can integer factorization be done in polynomial time?
• The Zarankiewicz problem : given m , n , s , t , how many edges can you put into a bipartite graph between m vertices and n vertices, such that there is no complete bipartite subgraph between s vertices or t vertices?
• The strong Aanderaa–Karp–Rosenberg conjecture
• The Erdős–Gyárfás conjecture : does every 3-regular graph have a simple cycle whose length is a power of two?
• Singmaster's conjecture : is there a constant bounding the maximal number of times that a number different from 1 may appear in Pascal's triangle?
• Tuza's conjecture : is it true that the smallest size of a subset of edges that hits all triangles of a graph is at most two times the largest number of edge-disjoint triangles that can be packed in the graph?
• Is it possible to solve graph coloring and computing maximum independent sets in polynomial time on even-hole-free graphs ?

Other lists of open problems ¶

• Open Problems - Graph Theory and Combinatorics
• Current Research Problems (William T. Trotter)
• List of unsolved problems in computer science (Wikipedia)
• Open Problem Garden
• Open problems on TCS.SE
• Major unsolved problems in theoretical computer science? (TCS.SE)
• Autobóz: Open Problems
• The PolyTCS project
• Are there any open problems left about DFAs?
• Open Problems in Sublinear Algorithms
• Not especially famous, long-open problems which anyone can understand
• The Open Problems Project
• Open problems in twin-width

Here are links to some other specific open questions found on other places on the Web:

• Équivalence des représentations de polyèdres convexes (in French)

Solved problems ¶

This section regroups problems that occurred in a previous version of this list, and were solved since then.

Complexity of an assignment problem with subsets ¶

It is known that a maximum matching can be found in PTIME. In particular, this is the case of bipartite graphs . However, what about the situation where we are allowed to remove vertices in one of the parts, and where we want to maximize the number of vertices that must remain unmatched in a maximum matching? What is the complexity of this problem?

• TCS.SE question with precise statement

Proved to be in PTIME by Chao Xu in this TCS.SE answer . Thanks!

Decidability of conjunctive query determinacy in the finite ¶

The query determinacy problem asks, given a set Q 1 , … , Q n of conjunctive queries (CQs) and an additional CQ Q , whether the Q i determine Q , i.e., whether, for any two (possibly infinite) relational databases I and I ′ , having Q i ( I ) = Q i ( I ′ ) for all 1 ≤ i ≤ n implies we must have Q ( I ) = Q ( I ′ ) . The query determinacy problem was shown 43 to be undecidable but this work left open the problem of finite determinacy , which is defined as determinacy except that I and I ′ must be finite.

Is finite determinacy also undecidable for conjunctive queries?

Proved by the authors of the original work 43 in a new paper . As this was accepted for publication at PODS 2016 , I think we can say that this has been accepted by the community, although I haven't personally checked the proof.

Steinberg's conjecture ¶

Grötzch's theorem says that planar graphs without 3-cycles ( triangles ) are 3- colorable . Is every planar graph without 4-cycles and 5-cycles 3-colorable?

Disproved in this paper . I haven't personally checked it, but it has been published in the Journal of Combinatorial Theory, so I'm assuming it is correct.

Feder-Vardi conjecture ¶

Letting Γ be a digraph , the CSP for Γ , written CSP ( Γ ) , is the following problem: given a digraph G , decide whether there is a homomorphism from G to Γ . The Feder-Vardi conjecture 34 asks: Is there a dichotomy on Γ , with CSP ( Γ ) being always either in PTIME or NP-hard?

An analogous result is already known for undirected graphs 35 , for some restricted classes of directed graphs 36 , and when Γ has two elements 37 or more recently three elements 38 .

Proved: two recent preprints by Bulatov and by Zhuk claim a proof of this result. The papers were accepted for publication at FOCS 2017 so I'm classifying this as solved (accepted by the community), even though it may still be a good idea to verify these proofs in more detail (see this post ). I have not personally checked any of this.

Thanks to Mikaël Monet for pointing out that the conjecture for digraphs implies 39 the conjecture for relational structures .

Complexity of counting linear extensions in posets of height 2 ¶

It is #P-hard to count the number of linear extensions of an input poset 2 . The proof uses posets of height  3, and leaves open the natural question: is it #P-hard to count linear extensions in posets of height 2?

An equivalent formulation is in terms of directed bipartite graphs (all edges go from one part to the other part): given a directed bipartite graph as input, is it #P-hard to count the number of topological sorts of the graph?

Solved in this paper (shown to be #P-hard). Note that I haven't personally checked it, and it does not seem to have been peer-reviewed yet. Thanks to Kuldeep S. Meel for pointing me to that paper.

Complexity of counting linear extensions in posets of dimension 2 ¶

This is similar to the question above, but for order dimension : is it #P-hard to count linear extensions in posets of dimension 2?

Solved in the same paper as above (shown to be #P-hard).

Retired problems ¶

This section contains former questions which I no longer think are interesting or sensible, or for which my interest has waned.

What is the connection between the fluted fragment and inversion-free queries? ¶

The fluted fragment is a fragment of function-free first-order logic for which the satisfiability problem is decidable 13 (but non-elementary). This definition is reminiscent of inversion-free queries , which are known 14 to be exactly the UCQs that admit OBDD lineages on TID databases (see this question for relevant definitions).

Is there any connection between these two classes?

The original version of this question incorrectly claimed that inversion-free queries are the positive existential fragment of fluted queries, but this is in fact not correct: there are non-hierarchical CQs, e.g., ∃ x y R ( x ) , S ( x , y ) , T ( y ) , which are fluted. So while there is still a connection in the definitions, the link is no longer as compelling, and I don't think the question is so interesting anymore.

Thanks to the anonymous Reviewer 3 of our paper at PODS 2016 for pointing out this connection. Thanks to Bartosz Bednarczyk for bringing back this problem to my attention, which made me realize the error.

Compactness difference between probabilistic XML document formalisms ¶

The PrXML formalism is a way to represent probability distribution on labeled, unranked, unordered trees 56 . It does so by representing uncertainty with special kinds of nodes:

• ind nodes have each child labeled with a probability in [ 0 , 1 ] indicating the probability (independently across draws) that the child node is kept, or that it is discarded along with its descendants; the ind node is replaced by the collection of its kept children;
• mux nodes have each child labeled with a probability in [ 0 , 1 ] , the probabilities summing to at most 1 , and one of the children is kept by drawing according to the probabilities (if the sum is < 1 there is a probability of keeping no child); the children that are not kept are removed with their descendants, and the mux node is replaced by its kept child (if any);
• det nodes are deterministically replaced by the collection of their children;
• cie nodes have their children labeled by a conjunction of Boolean variables from a global set of variables, where each variable has some probability in [ 0 , 1 ] of being true (the same variables can be used in multiple cie nodes); the semantics is that a valuation for the variables is drawn by setting each variable as true or false with the indicated probabilities, independently, and replacing each cie node by the children whose edge annotation evaluates to true under the chosen variable valuation;
• exp nodes are annotated with an explicit probability distribution: a set of pairs of a subset of children of the nodes and a probability, the probabilities summing to 1.

We give names to families of probabilistic XML documents according to the nodes that are allowed, e.g., PrXML ind , mux refers to probabilistic documents where nodes of type ind and mux are allowed. A family is efficiently translatable in another if any document of the first family can be rewritten to a document in the second. Some families are known to be efficiently translatable in others 57 , but open questions remain: is PrXML exp efficiently translatable in PrXML mux , det , or even to PrXML cie ?

Thanks to Pierre Senellart for helping me to prepare this entry.

Complexity of testing the equivalence of PrXML cie ¶

Using the previous definitions, the semantic equivalence problem for two PrXML documents asks whether the two documents define the same probability distribution on outcomes (same possible worlds, with same probabilities). Given two PrXML cie documents, what is the probability of deciding whether they are semantically equivalent? The problem is in EXPTIME but no lower bound or hardness result is known 58 . What is the complexity of this problem?

The structural equivalence problem asks, given two PrXML cie documents, whether, for each valuation of the variables, the corresponding valuations of both documents are the same. (Note that the probabilities assigned to the events is irrelevant.) The problem is in coNP, but no lower bound or hardness result is known 59 . What is the complexity of this problem?

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D. G. Corneil, M. Habib, J.-M. Lalignel, B. Reed, U. Rotics. Polynomial-time recognition of clique-width ≤ 3 graphs , 2012 (only available behind a paywall ).  ↩ ↩

P. Heggernes, D. Meister, U. Rotics. Computing the clique-width of large path powers in linear time via a new characterisation of clique-width ) ,  ↩

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J. Chuzhoy , Improved Bounds for the Excluded Grid Theorem , 2016. See Theorem 1.1, and the three following paragraphs.  ↩ ↩ ↩ ↩

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C. Chekuri, J. Chuzhoy. Polynomial Bounds for the Grid-Minor Theorem , 2014.  ↩

C. Chekuri, personal communication, 2015. (That's academic lingo to say that we emailed them and they don't know yet.)  ↩

J.-F. Baget, M. Bienvenu, M.-L. Mugnier, S. Rocher. Combining Existential Rules and Transitivity: Next Steps , 2015.  ↩

I. Pratt-Hartmann. Data-complexity of the two-variable fragment with counting quantifiers , 2009.  ↩ ↩

V. Bárány, G. Gottlob , M. Otto. Querying the Guarded Fragment , 2014.  ↩

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A. Calì, D. Lembo, R. Rosati. Query rewriting and answering under constraints in data integration systems , Theorem 3.4. However, the proof of this result has a slight inaccuracy; see Appendix A.2 of this paper for details.  ↩

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S. Felsner, T. Mészáros, P. Micek. Boolean dimension and tree-width , 2018.  ↩ ↩

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A. A. Bulatov. A dichotomy theorem for constraints on a three-element set , 2002.  ↩

T. Feder, M. Y. Vardi . The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory , 1998. See Theorem 10 and subsequent theorems.  ↩

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9 Real-World Problems that can be Solved by Machine Learning

Machine Learning has gained a lot of prominence in the recent years because of its ability to be applied across scores of industries to solve complex problems effectively and quickly. Contrary to what one might expect, Machine Learning use cases are not that difficult to come across. The most common examples of problems solved by machine learning are image tagging by Facebook and spam detection by email providers.

AI for business can resolve incredible challenges across industry domains by working with suitable datasets. In this post, we will learn about some typical problems solved by machine learning and how they enable businesses to leverage their data accurately.

What is Machine Learning?

A sub-area of artificial intelligence, machine learning, is an IT system's ability to recognize patterns in large databases to find solutions to problems without human intervention. It is an umbrella term for various techniques and tools to help computers learn and adapt independently.

Unlike traditional programming, a manually created program that uses input data and runs on a computer to produce the output, in Machine Learning or augmented analytics, the input data and output are given to an algorithm to create a program. It leads to powerful insights that can be used to predict future outcomes.

Machine learning algorithms do all that and more, using statistics to find patterns in vast amounts of data that encompass everything from images, numbers, words, etc. If the data can be stored digitally, it can be fed into a machine-learning algorithm to solve specific problems.

Types Of Machine Learning

Today, Machine Learning algorithms are primarily trained using three essential methods. These are categorized as three types of machine learning, as discussed below –

    1. Supervised Learning

One of the most elementary types of machine learning, supervised learning, is one where data is labeled to inform the machine about the exact patterns it should look for. Although the data needs to be labeled accurately for this method to work, supervised learning is compelling and provides excellent results when used in the right circumstances.

For instance, when we press play on a Netflix show, we’re informing the Machine Learning algorithm to find similar shows based on our preference.

How it works –

• The Machine Learning algorithm here is provided with a small training dataset to work with, which is a smaller part of the bigger dataset.
• It serves to give the algorithm an idea of the problem, solution, and various data points to be dealt with.
• The training dataset here is also very similar to the final dataset in its characteristics and offers the algorithm with the labeled parameters required for the problem.
• The Machine Learning algorithm then finds relationships between the given parameters, establishing a cause and effect relationship between the variables in the dataset.

    2. Unsupervised Learning

Unsupervised learning, as the name suggests, has no data labels. The machine looks for patterns randomly. It means that there is no human labor required to make the dataset machine-readable. It allows much larger datasets to be worked on by the program. Compared to supervised learning, unsupervised Machine Learning services aren’t much popular because of lesser applications in day-to-day life. 

How does it work?

• Since unsupervised learning does not have any labels to work off, it creates hidden structures.
• Relationships between data points are then perceived by the algorithm randomly or abstractly, with absolutely no input required from human beings.
• Instead of a specific, defined, and set problem statement, unsupervised learning algorithms can adapt to the data by changing hidden structures dynamically.

    3. Reinforcement Learning

Reinforcement learning primarily describes a class of machine learning problems where an agent operates in an environment with no fixed training dataset. The agent must know how to work using feedback.

• Reinforcement learning features a machine learning algorithm that improves upon itself.
• It typically learns by trial and error to achieve a clear objective.
• In this Machine Learning algorithm, favorable outputs are reinforced or encouraged, whereas non-favorable outputs are discouraged.

9 Real-World Problems Solved by Machine Learning

Applications of Machine learning are many, including external (client-centric) applications such as product recommendation , customer service, and demand forecasts, and internally to help businesses improve products or speed up manual and time-consuming processes.

Machine learning algorithms are typically used in areas where the solution requires continuous improvement post-deployment. Adaptable machine learning solutions are incredibly dynamic and are adopted by companies across verticals.

Here we are discussing nine Machine Learning use cases –

    1. Identifying Spam

Spam identification is one of the most basic applications of machine learning. Most of our email inboxes also have an unsolicited, bulk, or spam inbox, where our email provider automatically filters unwanted spam emails. 

But how do they know that the email is spam?

They use a trained Machine Learning model to identify all the spam emails based on common characteristics such as the email, subject, and sender content. 

If you look at your email inbox carefully, you will realize that it is not very hard to pick out spam emails because they look very different from real emails. Machine learning techniques used nowadays can automatically filter these spam emails in a very successful way. 

Spam detection is one of the best and most common problems solved by Machine Learning. Neural networks employ content-based filtering to classify unwanted emails as spam. These neural networks are quite similar to the brain, with the ability to identify spam emails and messages.

    2. Making Product Recommendations

Recommender systems are one of the most characteristic and ubiquitous machine learning use cases in day-to-day life. These systems are used everywhere by search engines, e-commerce websites (Amazon), entertainment platforms (Google Play, Netflix), and multiple web & mobile apps.

Prominent online retailers like Amazon and eBay often show a list of recommended products individually for each of their consumers. These recommendations are typically based on behavioral data and parameters such as previous purchases, item views, page views, clicks, form fill-ins, purchases, item details (price, category), and contextual data (location, language, device), and browsing history.  

These recommender systems allow businesses to drive more traffic, increase customer engagement, reduce churn rate, deliver relevant content and boost profits. All such recommended products are based on a machine learning model’s analysis of customer’s behavioral data. It is an excellent way for online retailers to offer extra value and enjoy various upselling opportunities using machine learning.

    3. Customer Segmentation

Customer segmentation, churn prediction and customer lifetime value (LTV) prediction are the main challenges faced by any marketer. Businesses have a huge amount of marketing relevant data from various sources such as email campaigns, website visitors and lead data.

Using data mining and machine learning , an accurate prediction for individual marketing offers and incentives can be achieved. Using ML, savvy marketers can eliminate guesswork involved in data-driven marketing.

For example, given the pattern of behavior by a user during a trial period and the past behaviors of all users, identifying chances of conversion to paid version can be predicted. A model of this decision problem would allow a program to trigger customer interventions to persuade the customer to convert early or better engage in the trial.

    4. Image & Video Recognition

Advances in deep learning (a subset of machine learning) have stimulated rapid progress in image & video recognition techniques over the past few years. They are used for multiple areas, including object detection, face recognition, text detection, visual search, logo and landmark detection, and image composition.

Since machines are good at processing images, Machine Learning algorithms can train Deep Learning frameworks to recognize and classify images in the dataset with much more accuracy than humans. 

Similar to image recognition , companies such as Shutterstock , eBay , Salesforce , Amazon , and Facebook use Machine Learning for video recognition where videos are broken down frame by frame and classified as individual digital images.

    5. Fraudulent Transactions

Fraudulent banking transactions are quite a common occurrence today. However, it is not feasible (in terms of cost involved and efficiency) to investigate every transaction for fraud, translating to a poor customer service experience.

Machine Learning in finance can automatically build super-accurate predictive maintenance models to identify and prioritize all kinds of possible fraudulent activities. Businesses can then create a data-based queue and investigate the high priority incidents.

It allows you to deploy resources in an area where you will see the greatest return on your investigative investment. Further, it also helps you optimize customer satisfaction by protecting their accounts and not challenging valid transactions. Such fraud detection using machine learning can help banks and financial organizations save money on disputes/chargebacks as one can train Machine Learning models to flag transactions that appear fraudulent based on specific characteristics.

    6. Demand Forecasting

The concept of demand forecasting is used in multiple industries, from retail and e-commerce to manufacturing and transportation. It feeds historical data to Machine Learning algorithms and models to predict the number of products, services, power, and more.

It allows businesses to efficiently collect and process data from the entire supply chain, reducing overheads and increasing efficiency.

ML-powered demand forecasting is very accurate, rapid, and transparent. Businesses can generate meaningful insights from a constant stream of supply/demand data and adapt to changes accordingly. 

    7. Virtual Personal Assistant

From Alexa and Google Assistant to Cortana and Siri, we have multiple virtual personal assistants to find accurate information using our voice instruction, such as calling someone, opening an email, scheduling an appointment, and more.

These virtual assistants use Machine Learning algorithms for recording our voice instructions, sending them over the server to a cloud, followed by decoding them using Machine Learning algorithms and acting accordingly.

    8. Sentiment Analysis

Sentiment analysis is one of the beneficial and real-time machine learning applications that help determine the emotion or opinion of the speaker or the writer. 

For instance, if you’ve written a review, email, or any other form of a document, a sentiment analyzer will be able to assess the actual thought and tone of the text. This sentiment analysis application can be used to analyze decision-making applications, review-based websites, and more.

    9. Customer Service Automation

Managing an increasing number of online customer interactions has become a pain point for most businesses. It is because they simply don’t have the customer support staff available to deal with the sheer number of inquiries they receive daily.

Machine learning algorithms have made it possible and super easy for chatbots and other similar automated systems to fill this gap. This application of machine learning enables companies to automate routine and low priority tasks, freeing up their employees to manage more high-level customer service tasks. 

Further, Machine Learning technology can access the data, interpret behaviors and recognize the patterns easily. This could also be used for customer support systems that can work identical to a real human being and solve all of the customers’ unique queries. The Machine Learning models behind these voice assistants are trained on human languages and variations in the human voice because it has to efficiently translate the voice to words and then make an on-topic and intelligent response.

If implemented the right way, problems solved by machine learning can streamline the entire process of customer issue resolution and offer much-needed assistance along with enhanced customer satisfaction.

Top 4 Issues with Implementing Machine Learning

While Machine learning is extensively used across industries to make data-driven decisions, its implementation observes many problems that must be addressed. Here’s a list of organizations' most common  machine learning challenges when inculcating ML in their operations.

1. Inadequate Training Data

Data plays a critical role in the training and processing of machine learning algorithms. Many data scientists attest that insufficient, inconsistent, and unclean data can considerably hamper the efficacy of ML algorithms.

2. Underfitting of Training Data

This anomaly occurs when data fails to link the input and output variables explicitly. In simpler terms, it means trying to fit in an undersized t-shirt. It indicates that data isn’t too coherent to forge a precise relationship.

3. Overfitting of Training Data

Overfitting denotes an ML model trained with enormous amounts of data that negatively affects performance. It's similar to trying an oversized jeans.

4. Delayed Implementation

ML models offer efficient results but consume a lot of time due to data overload, slow programs, and excessive requirements. Additionally, they demand timely monitoring and maintenance to deliver the best output.

Wrapping Up

As advancements in machine learning evolve, the range of use cases and applications of machine learning too will expand. To effectively navigate the business issues in this new decade, it’s worth keeping an eye on how machine learning applications can be deployed across business domains to reduce costs, improve efficiency and deliver better user experiences.

However, to implement machine learning accurately in your organization, it is imperative to have a trustworthy partner with deep-domain expertise. At Maruti Techlabs, we offer advanced machine learning services that involve understanding the complexity of varied business issues, identifying the existing gaps, and offering efficient and effective tech solutions to manage these challenges.

If you wish to learn more about how machine learning solutions can increase productivity and automate business processes for your business, get in touch with us .

1. What are the problems solved by machine learning?

The following types of problems are typically solved by machine learning:

• Identifying Spam: Filters spam emails automatically.
• Product Recommendations: Suggests products based on customer behavior.
• Customer Segmentation: Groups customers for targeted marketing.
• Image & Video Recognition: Recognizes and classifies images and videos.
• Fraud Detection: Identifies fraudulent transactions.
• Demand Forecasting: Predicts product demand.
• Virtual Assistants: Powers tools like Alexa and Siri.
• Sentiment Analysis: Analyzes emotions in text.
• Customer Service Automation: Automates routine inquiries.

2. What are machine learning problem statements?

Now that you know the various real-world problems machine learning can solve, if you have your project requirements ready, you can start creating your problem statements to help your development team better understand what you aim to achieve - just as you make business problem statements. Here is an example of a healthcare machine learning problem statement - Develop a machine learning model to predict patient readmissions within 30 days of discharge from the hospital. The model should analyze patient records, including demographics, medical history, treatment received, and post-discharge care.

Pinakin is the VP of Data Science and Technology at Maruti Techlabs. With about two decades of experience leading diverse teams and projects, his technological competence is unmatched.

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Statement of Purpose for PhD in Computer Science: 2 MIT Samples

• Posted on February 9, 2023

If you are reading this, you’re probably thinking of applying to Computer Science PhD programs.

We’ve prepared this guide to specifically help you navigate the challenging task of writing a statement of purpose for PhD in computer science.

We’ve used three SOPs, two of which were accepted at MIT and one at the University of Washington .

Obviously, these three SOPs are in no way representative of the full range of statements of purpose that get acceptance at top universities.

Therefore, if the profiles represented are different from yours, don’t get discouraged.

However, regardless of your background, we’d advise that you pay special attention to the structure and language used.

From our experience, many applicants fumble with how they describe their background and experiences.

We hope that won’t be the case anymore after reading our analysis and samples.

The samples used here were generously shared by people who are now students at MIT and University of Washington.

We therefore do not own any rights to the statements of purpose.

Our objective is to use these SOPs for educational purposes especially to help those affected by information asymmetry and the uneven distribution of educational resources.

We’re now offering one-on-one expert guidance on how to write a statement of purpose. This is in addition to our reviewing, editing, and standardizing services. Check out our ordering page , fill out the required details and let us help you craft a statement of purpose that will flood your email with admission offers. phdstatementsofpurpose.com

Side Note: Does your recommender need a guide/sample? We’ve created this for him/her

Letters of Recommendation: A Necessary Guide and Sample

How to start a Statement of Purpose for PhD in Computer Science

Before you start writing a statement of purpose, or any other admission essay, you need to prepare.

In preparing, the first place to start is looking at whether the university or program you’re applying to have specific requirements for their statement of purpose.

The requirements at MIT may vary from those at University of Chicago.

Look at the example below.

MIT has specific prompts or areas that your statement of purpose, called statement of objectives, must cover.

On the contrary, the University of Washington gives the word limit only, leaving you to describe your suitability for the program using the universal formula .

TAKE AWAY: Visit the university/program website to check if they have specific prompts to be followed. Follow these prompts to the letter. We recommend that you copy paste the requirements into your document so that you can always crosscheck to ensure you’re on track.

Introductory Narrative

Like with many other genres, writing the introduction to a Statement of Purpose for PhD in Computer Science is challenging.

Yet its importance cannot be stated enough as it sets the tone for the statement of purpose.

A bland and boring introduction may undermine a rich repertoire of experience and skills documented in subsequent parts.

From experience, all the statements of purpose we’ve reviewed and read start with one of the two formulae.

The first is a personal story that describes the applicants’ interest in the subject and field of study.

Childhood stories are also common as an introductory framework. We however do not encourage their use. A childhood story or personal story may set you apart as a human being but not as a PhD candidate.

If you must use them, make them credible and authentic and ensure that they are seamlessly linked to your research interest.

We’ve previously analyzed an MIT accepted Biomedical Engineering SoP that started off with a personal/childhood story so it’s no deal breaker.

The second approach, which we’d recommend, is to broadly state your research goals. This may be in the form of an unresolved problem in your area of interest. It may also take the form of an intriguing problem that you need to explore more about.

Let’s look at how these applicants have framed their introductory narratives.

MIT Accepted SoP for PhD in CS (1)

Explanation:

This SoP starts with a series of questions. The applicant then states the research interests and the broad goals of pursing a PhD in computer science.

University of Washington Accepted SoP for PhD in CS

The applicant goes straight to the research interests. The motivation for pursuing a PhD is broadly stated followed by future goals.

MIT Accepted SoP for PhD in CS (2)

This applicant starts with a one liner that states the research interest.

TAKE AWAY: There are different ways of starting a statement of purpose for PhD in computer science. Whichever method you use, make sure that you state your PURPOSE for applying aka your research interest.

Qualifications/experiences/motivation

This is the section of the SoP where you brand yourself.

The admission committee will probably sieve through thousands of applications. It’s therefore in your best interest to make it easy for them to determine straightaway that you are qualified for the program.

Therefore, be direct when talking about your experiences, accomplishments, and qualifications.

From our experience, creating a personal narrative is one of the most effective ways of creating a compelling statement of purpose.

We recommend a chronological way of describing your qualifications and experiences as this reflects your personal and professional growth.

You can start with your undergraduate work, professional engagements, relevant extracurricular, awards, and publications.

Please note carefully that how you describe your experiences may set you apart from other candidates.

Before we examine how the SoPs under examination here have described their experiences, it’s important that we list these tips for your benefit.

• Describe where you’ve demonstrated accomplishments, leadership, and collaboration
• State concrete achievements from these experiences
• Quantify your experiences for instance by showing numbers
• Show the impact of your work
• Describe actions as opposed to emotional state
• Explain the meaning of your experiences

We’ll explain these tips shortly as we highlight how they have been employed in our samples.

What makes this SOP for PhD in CS so special?

In this SoP that was accepted at MIT, the applicant describes the experience in a chronological manner, showing how she has grown as a person and a student/scholar.

She mentions the professors she has worked with, an aspect which enhances the credibility of her experience.

Remember that the adcom is not just interested in your academic suitability but also how you’ll fit it as part of a team.

The use of “we” in this SOP underlines the applicant’s collaborative skills.

She doesn’t hesitate to flaunt her achievements or roles when she uses “I”.

Her personality (resilience) is captured where she describes how she learned from disappointments.

Her growth as a researcher is captured in the second paragraph where she states that her first project left her with unanswered questions which she hoped the second project would help answer.

Notice also how she mentions her publications as culmination of research work.

Also noticeable is the repeated use of strong verbs such as contributed, learned, presented, collected, actualized, recommended, modeled etc.

Her research work has quantifiable impact and has led to her present research interest.

Moreover, the applicant has described other relevant experiences namely leadership and mentoring.

Her leadership and mentoring roles are aligned with her research interests as shown in the fourth paragraph where she also continues to use strong action verbs to underscore the impact of her work.

Importantly, the applicant has explained why every research she has undertaken is important and the significance of the research she will now pursue.

What makes this SoP special?

In this Statement of purpose for PhD in computer science that was accepted at the University of Washington, the applicant also captures her experience in a chronological manner showing how she has grown both as a person and a researcher.

She goes ahead to explain why her experiences matter, something that many applicants overlook. Pay attention to the second paragraph below where she explains that from her work as an undergraduate researcher, she learned two things namely research skills and approaches that formed the foundation of her future work.

In describing her interests, the applicant does not shy away from explaining areas where she has struggled.

Some applicants assume that for the SOP to be compelling, they must have everything figured out. The AdCom does not expect that you know everything otherwise you wouldn’t have applied.

In fact, highlighting areas where you have struggles open a window for you to explain how the university and the program will help you.

Like in SOP 1, the applicant has used strong action verbs.

Notable also is that for each area of research interest the applicant has described, there’s an explanation of what she has done and what she intends to do.

This last SoP that was accepted at MIT follows the same chronological pattern as the previous two.

The applicant names people she has worked with, the nature of the research, and outcomes, which are important publications and presentations.

In describing her experiences, she highlights the challenges he encountered and how she solved them.

Note the use of “we” to bring out collaborative skills as well as the heavy presence of strong action verbs in the SOP.

In paragraph 3 in particular, the applicant employs one of the tips we shared earlier about using concrete as opposed to vague experience: “I was one of the three winners…..”

Fitness for the Program and Future Goals

It’s of vital importance to describe why you’re a good fit for the program you’re applying to.

Do your research about some of the professors whose work align with your interest and describe exactly how you’ll work together.

It’s always recommendable to have several professors as long as you can justify why you want to work with them.

Don’t just state that your interests are aligned.

Remember the goal is to show not to state.

With the career/future goals, make sure that the AdCom can see your future trajectory.

Describe the big human problem you want to solve and how this program will help with that. Below is a snapshot of how the three applicants wrote their fitness and future goals section.

From the three Statement of purpose for PhD in Computer science, we can summarize the formula thus:

• Introduction: State your research interest
• Describe your experiences, qualifications, and relevant extracurricular activities. Use concrete and quantifiable experiences, state the outcomes, and use strong action verbs to underscore your roles.
• Describe your fitness for the program and future goals.

Still have a question about your Statement of purpose for PhD in computer science? We’re here to help.

Written your Statement of purpose but are still anxious about whether it meets the highest standards required? You can speak to us. Check below our reviewing and editing checklist and drop us your draft and prompts followed for a review by ORDERING HERE

Our Reviewing Checklist

• Is the introductory narrative authentic, relevant, credible, and how well is it linked to your research interests?
• How well have you covered your background/qualifications? Have you used quantifiable and concrete experiences?
• In describing your experiences, have you employed a simple but effective formula typical  of well written SOPs that get acceptance to top programs?
• Have you anticipated potential deficiencies in your background and how well have you addressed them?
• Have you explained ‘why this program’ and have you made any of the common mistakes we see a lot in this section?
• Are your career goals described using the SMART model?
• Does your conclusion cover the big problem you’re going to help solve and how the program will help you?

Our Editing Checklist

Our editing services transform your Statement of Purpose:

• IDEAS-From fuzzy, disjointed, and sketchy to clear, focused and rich in detail
• ORGANIZATION-From incoherent with no lead to great lead, logical, coherent, and powerful end.
• VOICE-From boring, bland, and cliched to enthusiastic and gripping
• WORD CHOICE-From tired and overused words to strong verbs, clear nouns, and well chosen modifiers.
• CONVENTIONS-From numerous distracting errors to editorial correctness.
• SENTENCE FLUENCY-From bumpy, hard to read to easy to read.

Step by step Analysis of MIT accepted SoP for CS (1)

Samples in other subjects

Nursing (PhD), Cognitive Science, Computer Science (undergraduate), Pyschology (PhD) and MBA

Statement of Purpose for Business Management

Statement of Purpose for Mathematics

Statement of Purpose for MPH and MBA with Engineering Background

Statement of Purpose for Nursing (undergraduate)

Statement of Purpose for MBA Ivy

• SOP for MBA
• SOP for Law Internship
• SOP for Tourism
• SOP for Social Work

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How to formulate good problem statements in CS research

Short background: I started my PhD last November and now I am helping a master student writing his MSc thesis. I still have problems when I need to formulate a concise research question and even, at least in workshop papers, some publications fail in formulating clear research questions as well. The topic the CS student writes about is the following. There is this work by Bracha on pluggable / optional type systems, e.g. for scripting languages. The student wants to solve the same problem that these 'pluggable typesystem' solves. But he is using dependent-type theory, i.e., to check that values in the scripting language are valid according to a given type. This can solve (or better solve) problems related to scripting languages (e.g. security problems in web programming; because everything is basically a string in scripting languages).

I find it hard to come up with a concise research question. (And possibly also with a method to evaluate the approach).

So, my question is:

• Are there any references that can help me to formulate valid research questions?

The closest reference I have found is this mini-tutorial by Mary Shaw.

From Germany there is also a Memorandum that is interesting, but the focus is only on information systems research and not CS. (I can't find a link to the long version in either English or German yet.)

• research-process
• computer-science
• reference-request

• You mean something like this ? (What does your advisor have to say about that? I guess he shifted this supervision on you?) –  Raphael Commented Aug 29, 2012 at 20:51
• This paper is advice on how to properly referee/review a paper. In turn, it shows how to properly write a good research paper. –  Nicholas Mancuso Commented Aug 30, 2012 at 0:51
• This seems at least a little area-specific, especially between more "systems" and more "theory" oriented parts of CS. –  Suresh Commented Aug 30, 2012 at 8:33
• 1 Another thing: look at (important) paperes of the field. They usually contain "open questions" or "future research". Try to figure out what the big players thought interesting but have not done yet, and start from there. –  Raphael Commented Aug 30, 2012 at 21:27
• 6 Often the correct problem formulation only becomes clear after you have the solution in hand. It's relatively rare to actually solve the precise problem that you set out in advance to solve. (Or maybe that's just me.) –  JeffE Commented Sep 1, 2012 at 15:46

3 Answers 3

Have you tried the following:

Turabian, Kate L. A Manual for Writers. Chicago: University of Chicago, 1987. Print.

It's a very nice book and is applicable to CS (unlike many other research methodology books).

• Formulating good research problems comes from experience. If you understand an area well, you will see the fundamental concepts. From there, your problem statement is simply an articulation of these concepts. For a beginner, this is very hard. Advice: try to cut down the problems into sub-problems. Some will be easy, and some will be 'hard', and solving them means the rests become easy or open new doors. So construct a work breakdown structure (WBS).
• Try to formalize the problem; i.e., derive a mathematical model for the problem at hand. This will help focus your mind on key concepts or variables. For example, for an optimization problem, you might decide on an objective function, and after that determine all relevant constraints. This will be an iterative process.
• Start with a toy example, with as many assumptions that you need to make it a toy example. Then slowly generalize and once you have enough intuition, then formulate the key problem to be solved.

Problem formulation is crucial phase in the research process. It start from; what is known at certain point of time and what is gape/defect/uncertainty/challenge/weakness in existing knowledge/system/model/solution or answer to a quest. Also Problem formulation starts from thrust/quest/hunger for new knowledge/knowing to unknown or need for exploration/extension/enhancement of the existing knowledge at a point of time. Finally Problem formulation precisely needs to define and draft the statement of the weakness in aforementioned knowledge using crystal clear words with preferably directional hypothesis. In statement it should cover 1)what is required?, 2) desired inputs and outputs with desired features and inter-linkage.

• 2 I reviewed this answer because someone raised a Low Quality Posts flag. I must admit I failed to see why it's bad. It's not a spam nor abusive. I could not find any source it came from, i.e. it might not be plagiarized from somewhere. Would the downvoters explain why it's bad? Thanks. –  Nobody Commented Dec 11, 2017 at 3:06
• @scaaahu I was the VLQ, but I didn't vote it down. I did it because I found it hard to understand. (Btw, the flag became "disputed".) Probably the downvoters had the same reason. Now I think maybe I was too eager to flag it, my habit is nicer in general. –  peterh Commented Dec 11, 2017 at 7:34
• @peterh Thanks for replying. I was afraid I was missing something so I asked the question. Now, I understand. Yes, I agree this post was hard to understand. But, please trust me, I have reviewed thousands of posts and many of them are much more incomprehensible than this one. Sorry about the disputed flag. –  Nobody Commented Dec 11, 2017 at 7:52

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Computer Science and Engineering Theses and Dissertations

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Previous Year Questions: Propositional Logic | Engineering Mathematics for Computer Science Engineering - Computer Science Engineering (CSE) PDF Download

Q1:  L et p and q be the following propositions: p : Fail grade can be given. q : Student scores more than 50% marks. Consider the statement: "Fail grade cannot be given when student scores more than 50% marks." Which one of the following is the CORRECT representation of the above statement in propositional logic?  (2024 SET-2) (a)  q → ¬ p q → ¬p (b) q → p (c)  p → q p → q (d) ¬p → q Ans : (a) Sol: Q when P means P→Q. Given statement, P : Fail grade can be given. Q : Student score more than 50% marks. ¬P : Fail grade cannot be given So, Fail grade cannot be given when student score more than 50% marks. is written as  Q→¬P Correct answer is option A. Q2: Geetha has a conjecture about integers, which is of the form ∀x [P(x) ⇒ ∃yQ(x, y)] where P is a statement about integers, and Q is a statement about pairs of integers. Which of the following (one or more) option(s) would imply Geetha's conjecture?  (2023) (a)  ∃ x [ P ( x ) ∧ ∀ y Q ( x , y ) ] ∃x [P(x) ∧ ∀yQ (x, y)] (b) ∀x ∀yQ (x, y) (c) ∃y ∀x [P(x) ⇒ Q(x, y)] (d) ∃x [P(x) ∧ ∃yQ (x, y)] Ans: (b, c) Sol: Here, domain is the set of integers, So, elements x, y∈{...,−3, −2, −1, 0, 1, 2, 3,...} and assuming a tautology is defined as a formula or assertion that is true in every possible interpretation. Since, statement ∀x P(x) is same as P(1) ∧ P(2) ∧... and statement ∃xP(x) is same as P(1) ∨ P(2)∨... (Here, “...” contains all the elements from the domain, not only positive integers) and A implies B is true means A ⇒ B is a tautology. Some points can be noted as:

• Symbols  ∀(universal quantifier) is used for conjunction and ∃ (existential quantifier) is used for disjunction.
• ¬∀x¬ ≡ ∃x and ¬∃x¬ ≡ ∀x 
• Using Null Quantification, we can write ∀x (P(x) ⇒ ∃yQ (x, y)) as ∀x∃y(P(x) ⇒ Q(x, y)). Both are equivalent expressions.

Method 1: B. ∀x ∀yQ(x, y) ⇒ [∀x (P(x) ⇒ ∃yQ(x, y))]

≡ ∀x ∀yQ(x, y) ⇒ [∀x ∃y(P(x) ⇒ Q(x, y))]

≡ ∀x ∀yQ(x, y) ⇒ [∀x ∃y(¬P(x) ∨ Q(x, y))]

≡ ∀x ∀yQ(x, y) ⇒ [∀x(¬∀y(P(x) ∧ ¬Q(x, y))] Now, both sides of ⇒ there are ∀ (universal) quantifier and which is used for conjunction. If we try to make left side true then right side should also be true to become this formula as tautology. So, left side is true when Q(x, y) is true for each x, y from the domain and so in right side, ¬Q(x, y) becomes false and so, P(x) ∧ ¬Q(x, y) becomes false and so, ¬∀y(P(x) ∧ ¬Q(x, y) becomes true and so, ∀x(¬∀y(P(x) ∧ ¬Q(x, y)) becomes true.   Hence, when left side is true then right sides is also true and so, it is a tautology and so, B is correct. C.  ∃y∀x (P(x) ⇒ Q(x, y)) ⇒ [∀x(P(x) ⇒ ∃yQ(x, y))] ≡ ∃y∀x(P(x) ⇒ Q(x, y)) ⇒ [∀x∃y(P(x) ⇒ Q(x, y))] ≡ ∃y∀xR(x, y) ⇒ ∀x∃yR(x, y) Now, Consider the interpretation of R(x, y) as x + y = 0. Now, ∃y∀xR(x, y) means that “There exist an integer y such that for every ineger x, R(x, y)” which is false because if we choose any y then there will be “only one” x. In the same way, ∀x∃yR(x, y) is true because for every x there exist a y such that x + y = 0. ∃y∀xR(x, y) is true if and only if there exist a y which makes R(x, y) true for every x. So, y does not depend on x. ∀x∃yR(x, y) is true if and only if there exist a y which makes R(x, y) true for every x. So, y does not depend on x. So, ∃y∀xR(x, y) is stronger than ∀x∃yR(x, y). Hence, if ∃y∀xR(x, y) is true then ∀x∃yR(x, y) must also be true but if ∀x∃yR(x, y) is true then ∃y∀xR(x, y) need not be true as can be seen from above interpretation of  x + y = 0.

A. ∃x(P(x) ∧ ∀yQ(x, y)) ⇒ [∀x(P(x) ⇒ ∃yQ(x, y))]

≡ ¬∀x[P(x) ⇒ ∃y¬Q(x, y)] ⇒ [∀x(P(x)⇒ ∃yQ(x, y))] ≡ ¬[P(1) ⇒ ∃y ¬ Q(1, y) ∧ P(2) ⇒ ∃y ¬ Q(2, y) ∧...] ⇒ [P(1) ⇒ ∃yQ(1, y) ∧ P(2) ⇒ ∃yQ(2, y)∧...] Now, assign P(1) and P(2) as True and Q(1, y) is False for every y and Q(2, y) is True for every y which makes right side of ⇒ as False and left side as True. Hence, it is not a tautology.

D. ∃x(P(x) ∧ ∃yQ(x, y)) ⇒ [∀x(P(x) ⇒ ∃yQ(x, y))]

• There exists some boys who have girlfriends.  (True)
• There exists some boys for whom all the girls are girlfriend. (False)
• For all boys there exists a girlfriend. (False)
• For all girls, there exists a boyfriend (True) (Same as given statement F)

• x is a perfect square and x is a prime number, this can never be true as every square has at least 3 factors, 1, x and x 2 .

So, second condition can never be true. which implies the first condition must be true. x ∈ {8, 9, 10, 11, 12} AND x is not a composite number But here only 11 is not a composite number. so only 11 satisfies the above statement. ANSWER 11. Q17: In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it. Upon asking, the person replies the following "The result of the toss is head if and only if I am telling the truth." Which of the following options is correct?  (2015 SET-3) (a) The result is head (b) The result is tail (c) If the person is of Type 2, then the result is tail (d) If the person is of Type 1, then the result is tail Ans: (a) Sol:  We do not know the type of the person from whom those words are coming from and so can have two cases :

• Truth-teller : definitely implies that result of toss is Head.
• Liar : the reality will be the negation of the statement.

The negation of (x⟺y) is exactly one of x or y holds. So, we negate the statement : "The result of the toss is head if and only if I am telling the truth". This give rise to two possibilities

• it is head and lie spoken
• it is not head and truth spoken

Clearly the second one cannot be true because it cannot be a reality that the liar speaks the truth. So, this implies that even if we negate the statement to see the reality or don't do that; The reality is that the toss yielded a Head. Answer = option (A). Q18: Which one of the following well formed formulae is a tautology?  (2015 SET-2) (a) ∀x ∃y R (x, y) ↔ ∃y ∀x R(x, y) (b) (∀x [∃y R(x, y) → S(x, y)]) → ∀x ∃y S(x, y) (c)  [ ∀ x ∃ y P ( x , y ) → R ( x , y ) ] ↔ [ ∀ x ∃ y ( ¬ P ( x , y ) ) ∨ R ( x , y ) ] [∀x ∃y P(x, y) → R(x, y)] ↔ [∀x ∃y(¬P(x, y)) ∨ R(x, y)] (d) ∀x ∀y P(x, y) → ∀x ∀y P(y, x) Ans:  (c) Sol:  NOTE: “Tautology" & “Valid" are Different Concepts in First Order Logic. Tautology & Valid are Same Concepts in Propositional Logic. Watch the following Detailed Lecture on  “Tautology Vs Valid” in First Order Logic: Note 1 : When no information is given about Domain of variables for a First Order Logic (FOL) formula, then consider that domain for all variables in the given FOL formula is same. Unless otherwise explicitly stated, domain should be taken same for all variables of a given FOL formula. Note 2 : For propositional logic(PL) / Sentential logic, “Tautology” of an expression means same thing as “Validity” of that expression. But this is Not true in FOL. Tautology/Validity in Propositional Logic : Tautologies are a key concept in propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. Given propositional logic expression (PLE) G is said to be Valid or Tautology iff G is ALWAYS True, regardless of which valuation is used for the propositional variables. Some examples of Tautologies in PL : A∨¬A (A∨B)→(A∨B) (A→B)→(¬B→¬A) In propositional logic, there is no distinction between a tautology and a logically valid formula. So, In Propositional logic : Valid ≡ Tautology ≡ True Tautology/Validity in First Order Logic(FOL) : From Wikipedia : The definition of tautology can be extended to sentences in predicate logic, which may contain quantifiers—a feature absent from sentences of propositional logic. Indeed, in propositional logic, there is no distinction between a tautology and a logically valid formula. In the context of predicate logic, many authors define a tautology to be a sentence that can be obtained by taking a tautology of propositional logic, and uniformly replacing each propositional variable by a first-order formula (one formula per propositional variable). The set of such formulas is a proper subset of the set of logically valid sentences of predicate logic (i.e., sentences that are true in every model). The fundamental definition of a tautology is in the context of propositional logic. The definition can be extended, however, to sentences in first-order logic. These sentences may contain quantifiers, unlike sentences of propositional logic. In the context of first-order logic, a distinction is maintained between logical validities, sentences that are true in every model, and tautologies, which are a proper subset of the first-order logical validities. In the context of propositional logic, these two terms coincide. A tautology in first-order logic is a sentence that can be obtained by taking a tautology of propositional logic and uniformly replacing each propositional variable by a first-order formula (one formula per propositional variable). (Note that Propositional logic manipulations can be done on the given formula, but No FOL manipulation should be done.) For example, because A ∨ ¬A is a tautology of propositional logic,  (∀x(x = x)) ∨ ¬(∀x(x = x)) is a tautology in first order logic. Example 2: [(∀y¬Py → ¬Px) → (Px → ¬∀y¬Py)] is a FOL Tautology. because it can be obtained from a contraposition tautology  (A → ¬B) → (B → ¬A) by replacing A by ∀y¬Py and B by Px. Example 3: ∀x ∀yP(x, y) → ∀x ∀yP(x, y) is a FOL tautology because it can be obtained from a PL Tautology A → A by replacing A with ∀x ∀y P(x, y). Not all logical validities are tautologies in first-order logic. For example, the sentence (∀x Rx) → ¬∃x ¬Rx

is true/valid in any first-order interpretation BUT it is Not a FOL Tautology, because it corresponds to the propositional sentence A→B  which is not a tautology of propositional logic.

• A : Good mobile phones.
• B : Cheap mobile phones.

P:(A → ¬B) ⟺ (¬A ∨ ¬B) Q:(B → ¬A) ⟺ ((¬B ∨ ¬A) ⟺ ¬A ∨ ¬B)) (Disjunction is commutative), Hence, (P ⟺ Q) which means (P → Q) and (Q → P). Q24: Which one of the following Boolean expressions is NOT a tautology?  (2014 SET-2) (a)  ( ( a → b ) ∧ ( b → c ) ) → ( a → c ) ((a → b) ∧ (b → c)) → (a → c) (b) (a → c) → (∼b → (a ∧ c)) (c) (a ∧ b ∧ c) → (c ∧ a) (d) a → (b → a) Ans: (b) Sol: Another way to solve it... Implication A → B is not tautology if B is false and A is true. For b option Let RHS ie. b → (a ∧ c) be false ie b is false and (a ∧ c) is false. Now, a ∧ c is false if either one of them is false. Now, if a and c both are false then a → c is true. LHS is true and RHS is false. So option b is not tautology. Q25: Which one of the following propositional logic formulas is TRUE when exactly two of p, q, and r are TRUE?  (2014 SET-1) (a) ((p ↔ q) ∧ r) ∨ (p ∧ q ∧ ∼ r) (b)  ( ∼ ( p ↔ q ) ∧ r ) ∨ ( p ∧ q ∧ ∼ r ) (∼ (p ↔ q) ∧ r) ∨ (p ∧ q ∧ ∼ r) (c) ((p → q) ∧ r) ∨ (p ∧ q ∧ ∼ r) (d) (∼(p ↔ q) ∧ r) ∧ (p ∧ q ∧ ∼ r ) Ans: (b) Sol:  A. will be true if P, Q, R are true, ((p ↔ q) ∧ r) will return true. So "exactly two" is false C. if only r is true and p and q are false, first part of implication itself will result in true D. if r is true or false, this returns false due to r and ¬r present in conjunction. So, this is a CONTRADICTION. B is the answer. B is true if p is TRUE and q is FALSE or vice verse, and r is true or if p and q are TRUE and r is FALSE. PS: Actually the question should have been "TRUE ONLY when exactly two of p, q and r are TRUE". Q26: Consider the statement "Not all that glitters is gold" Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?  (2014 SET-1) (a) ∀x : glitters(x) ⇒ ¬gold(x) (b) ∀x : gold(x) ⇒ glitters(x) (c)  ∃ x : g o l d ( x ) ∧ ¬ g l i t t e r s ( x ) ∃x : gold(x) ∧ ¬glitters(x) (d) ∃x : glitters(x) ∧ ¬gold(x) Ans:  (d) Sol:  "Not all that glitters is gold”  can be expressed as : ¬(∀x(glitters(x) ⟹ gold(x))) (as restriction of universal quantification is same as universal quantification of a conditional statement.) "Not all that glitters is gold" means "some glitters are not gold" which can be expressed as   ∃x(glitters(x) ∧ ¬gold(x)) (as restriction of an existential quantification is same as existential quantification of a conjunction.) So option (D) is correct. Q27: Which one of the following is NOT logically equivalent to ¬∃x(∀y(α) ∧ ∀z(β))?  (2013) (a)  ∀ x ( ∃ z ( ¬ β ) → ∀ y ( α ) ) ∀x(∃z(¬β) → ∀y(α)) (b)  ∀ x ( ∀ z ( β ) → ∃ z ( ¬ α ) ) ∀x(∀z(β) → ∃z(¬α)) (c) ∀x(∀y(α) → ∃z(¬β)) (d) ∀x(∃y(¬α) → ∃z(¬β)) Ans:  (a, d) Sol: A useful rule: ∀x(α) = ¬∃(x)(¬α) i.e.; If some property α is true for all x, then it is equivalent ot say that no x exists such that property α does not hold for it. Starting with choices:

• ∀x(∃z(¬β) → ∀y(α)) ⇒ ∀x(¬∃z(¬β) ∨ ∀y(α)) ⇒ ∀x(∀z(β) ∨ ∀y(α)) ⇒ ¬∃x¬(∀z(β) ∨ ∀y(α)) ⇒ ¬∃x(¬∀z(β) ∧ ¬∀y(α)) So, A is not matching with the logical statement in question.
• ∀x(∀z(β) → ∃y(¬α)) ⇒∀ x(¬∀z(β) ∨ ∃y(¬α)) ⇒¬∃x¬(¬∀z(β) ∨ ∃y(¬α)) ⇒¬∃x(∀z(β) ∧ ¬∃y(¬α)) ⇒¬∃x(∀z(β) ∧ ∀y(α)) Hence, matches with the given statement.
• ∀x(∀y(α) → ∃z(¬β)) ⇒ ∀x(¬∀y(α) ∨ ∃z(¬β)) ⇒ ¬∃x¬(¬∀ y (α) ∨ ∃z(¬β)) ⇒ ¬∃x(∀y(α) ∧ ¬∃z(¬β)) ⇒ ¬∃x(∀y(α) ∧ ∀z(β)) Hence, matches with the given statement.
• ∀x(∃y(¬α) → ∃z(¬β)) ⇒ ∀x(¬∃y(¬α) ∨ ∃z(¬β)) ⇒ ∀x(∀y(α) ∨ ∃z(¬β)) ⇒ ¬∃x¬(∀y(α) ∨ ∃z(¬β)) ⇒ ¬∃x(¬∀y(α) ∧ ¬∃z(¬β)) ⇒ ¬∃x(¬∀y(α) ∧ ∀z(β)) So, D is not matching with the logical statement in question.

Thus both (A) and (D) are not logically equivalent to the given statement. In GATE 2013 marks were given to all for this question. Q28: What is the logical translation of the following statement? "None of my friends are perfect."  (2013) (a) ∃x(F(x) ∧ ¬P(x)) (b) ∃x(¬F(x) ∧ P(x)) (c) ∃x(¬F(x) ∧ ¬P(x)) (d) ¬∃x(F(x) ∧ P(x)) Ans: (d) Sol: 

• some of my friends are not perfect
• some of those who are not my friends are perfect
• some of those who are not my friends are not perfect
• NOT (some of my friends are perfect) / none of my friends are perfect

Correct Answer: D. Q29: What is the correct translation of the following statement into mathematical logic? "Some real numbers are rational"  (2012) (a)  ∃ x ( r e a l ( x ) ∨ r a t i o n a l ( x ) ) ∃x(real(x) ∨ rational(x)) (b) ∀x(real(x) → rational(x)) (c) ∃x(real(x) ∧ rational(x)) (d) ∃x(rational(x) → real(x)) Ans:  (c) Sol:  Meaning of each choices:

• There exists a number which is either real or rational
• If a number is real it is rational
• There exists a number which is real and rational
• There exists a number such that if it is rational, it is real

So, (C) is the answer.

Q30: Consider the following logical inferences.  I 1 : If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. I 2 : If it rains then the cricket match will not be played. It did not rain. Inference: The cricket match was played. Which of the following is TRUE?  (2012) (a) Both I 1 and I 2  are correct inferences (b) I 1 is correct but I 2 is not a correct inference (c) I 1 is not correct but I 2 is a correct inference (d) Both I 1 and I 2 are not correct inferences Ans: (b) Sol:  I 1 is a correct inference. I 2 is not a correct inference as it was not mentioned what would have happened if it hadn't rained- They might have played or they might not have played. Q31: Which one of the following options is CORRECT given three positive integers x, y and z, and a predicate P(x) = ¬(x = 1)  ∧ ∀y (∃z(x = y∗z)) ⇒ (y = x) ∨ ( y = 1)  (2011) (a) P(x) being true means that x is a prime number (b) P(x) being true means that x is a number other than 1 (c) P(x) is always true irrespective of the value of x (d) P(x) being true means that x has exactly two factors other than 1 and x Ans: (a) Sol: P(x) = (¬(x=1) ∧ ∀y(∃z(x = y∗z) ⟹ ((y = x) ∨ (y = 1))) Statement:  x is not equal to 1 and if there exists some z for all y such that product of y and z is x, then y is either the number itself or 1. This is the definition of prime numbers. Alternative approach: The formula ∃x ∀y ∀z[×(y, z, x) → ((y = 1) ∨ (z = 1))] expresses the statement "there exists a prime number" (the number 1 also satisfies this statement). Note here that × (y, z, x) is equivalent to (x = y × z). but ¬(x = 1) removes 1 as satisfying given number in question's formula, so the option (A) is True. Q32: Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula ∀x ∃y ∃t(¬F(x, y, t))?  (2010) (a) Everyone can fool some person at some time (b) No one can fool everyone all the time (c) Everyone cannot fool some person all the time (d) No one can fool some person at some time Ans: (b) Sol: F(x, y, t) ⇒ person x can fool person y at time t. For the sake of simplicity propagate negation sign outward by applying De Morgan's law. ∀x ∃y ∃t (¬F(x, y, t)) ≡ ¬∃x ∀y ∀t (F(x, y, t)) [By applying De Morgan's law.] Now converting ¬∃x ∀y ∀t(F(x, y, t)) to English is simple. ¬∃x ∀y ∀t(F(x, y, t)) ⟹ There does not exist a person who can fool everyone all the time. Which means No one can fool everyone all the time. So, option (B) is correct.

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My PhD Application Research Statement

I am committed to making the PhD application process more open and clearer to new students, since it is my view that the unnecessary opaqueness of the status quo mostly serves to discourage minorities from applying and to preserve power in the hands of elites. Therefore, I share below the personal statement I used when applying to graduate school in 2018, in hopes it may help someone down the road. I added some comments in square brackets to explain my intended purpose for each section.

Of course, it must come with a big disclaimer: I am not in any way claiming that this is a good statement, let alone a model for others’ statements, nor making any promises about your success if you follow this advice. Also, note that the fact that I am posting this online means that this text will appear in an online search, so you probably don’t want to copy specific words or phrases ;)

Personal Statement

To whom it may concern,

[This first paragraph is a very brief summary which answers the questions “who am I?”, “what am I applying for?”, “why should you hire me?” The rest of the statement serves as a justification for the pitch made in this paragraph.]

My name is Silvia González Sellán and I am a Mathematics and Physics undergraduate student with experience in Computer Graphics research at a high level. I am writing to apply to the direct entry PhD program, to hopefully begin in Fall 2019. I believe my previous achievements can vouch for my ability to proficiently participate in a world-renowned institution like University of Toronto, and I hope my interdisciplinary training can bring to it an innovative perspective.

[The next three paragraphs are “background”, and they are not specific to which University I am applying to. Their purpose is to show that I have the experience you’re looking for as a recruiter and I am confortable describing and discussing the details of my research. Also, detailing the specific responsabilities I took on with each project.]

By this summer I will be granted two individual Bachelor of Science degrees in both Mathematics and Physics. However, for the past two years I have been dedicating myself mostly to my Computer Graphics research, supervised by professor Alec Jacobson (University of Toronto) and partially funded by several Fields Institute of Mathematics programs. Specifically, I have focused on the subfield of Geometry Processing, working with two or three-dimensional shapes in the form of meshes and using mathematical tools to analyze and manipulate them.

In our latest finished project, we circumvented the problem of achieving solid meshes of complex domains by presenting a new way to define discrete differential operators on simpler meshes that make up the final domain via set operations. The applications of our method are manifold, from shape deformations to data smoothing to the computation of solid geodesic distances in a complicated shape. Our work has so far resulted in one high-level publication of which I am the first author, “Solid Geometry Processing on Deconstructed Domains”, which has been accepted with major revisions in the journal Computer Graphics Forum. I have also presented our results in poster format in several venues, like the 2018 Eurographics Symposium on Geometry Processing or the Graphics Interface 2018 conference. Lately, I have begun working on a new project, also supervised by professor Jacobson, involving morphological operations and geometric flows on surfaces, which is still on its early stages but the results of which we intend to submit for publication in Spring 2019.

[This ended up happening in Spring 2020!]

As the first author and the only student working on these projects for most of their duration, I took on the main responsibilities associated with them: with my supervisor’s assistance, we produced the necessary code and mathematical results and presented them in the most polished way possible, both in poster and paper form. I also worked on satisfying the reviewers’ comments during our first peer-review phase and submitted an improved version of our paper which complied with the major revisions required and is currently under review.

[This is the vision section. My intention was to tell the reader “You won’t need to worry about figuring out what to do with me, I have a very clear plan that you should be excited about”.]

If given the opportunity of working towards my PhD at University of Toronto, my vision for the program would be two-fold. My most immediate intention is to complete my reading and formal studies in order to achieve a global grasp of Computer Graphics as a field. Attending lectures in different congresses such as SIGGRAPH 2018 has woken me up to the very different avenues one can follow within it, and I would very much love to have a better understanding of these so I can choose my future wisely. Secondly, I would like to continue with my work in Geometry Processing and Discrete Differential Geometry, making use of your laboratory’s resources to collaborate with other scientists in order to produce high-quality research and have the satisfaction that I am significantly contributing to such a young, fast-growing area of knowledge like Graphics is.

[Now begins the institution-specific section of the statement. I thought it important to add concrete facts that relate me to the institution, and start from the bottom up: beginning with the specific supervisor (it is important to name them), then the Department and ending with the University as a whole.]

During the past two years I have cultivated a great relationship with the University of Toronto Department of Computer Science and, more specifically, with the Computer Graphics area of the Dynamic Graphics Project laboratory. Not only have I been directed by professor Alec Jacobson in two Fields Institute of Mathematics research programs, but this has also meant that I have spent a combined time of four months working in the DGP laboratory, directed by professor David Levin. I have also given research-related talks at the Department of Computer Science Undergraduate Summer Research Program (UGSRP) in 2017 and 2018, and even travelled to Toronto in the winter to attend and speak at the Toronto-Montreal Area Graphics Workshop (TOMOGRAPH) in late 2017, which was hosted by the same Department. In the upcoming years, I would be interested in being supervised by professor Jacobson or professor Levin in order to continue with our research together.

My excitement about participating in this Department’s PhD program is only matched by my desire to belong to University of Toronto’s community as a whole. I first visited St. George’s campus as a tourist during my first trip to Canada in 2013 and was captivated by its beauty as much as by its welcoming climate of tolerance. During my academic visits to the University in the following years I was privileged to interact and collaborate with various U of T graduate and undergraduate students, and it was thanks to them that I became determined that I am a great fit for Toronto’s academic and cultural community. The institution’s commitment to tackle gender-based harassment and create a diverse and inclusive environment has convinced me even more that I should present myself as a candidate for this position.

[Closing, standard language.]

I kindly ask that you consider my application for the PhD program to begin Fall 2019. I am looking forward to knowing your decision and remain at your disposal for any additional information you may request, as well as for an interview if you were to deem it helpful.

Yours faithfully,

Silvia González Sellán

Computer Science Thesis Topics

This page provides a comprehensive list of computer science thesis topics , carefully curated to support students in identifying and selecting innovative and relevant areas for their academic research. Whether you are at the beginning of your research journey or are seeking a specific area to explore further, this guide aims to serve as an essential resource. With an expansive array of topics spread across various sub-disciplines of computer science, this list is designed to meet a diverse range of interests and academic needs. From the complexities of artificial intelligence to the intricate designs of web development, each category is equipped with 40 specific topics, offering a breadth of possibilities to inspire your next big thesis project. Explore our guide to find not only a topic that resonates with your academic ambitions but also one that has the potential to contribute significantly to the field of computer science.

1000 Computer Science Thesis Topics and Ideas

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Get 10% off with 24start discount code, browse computer science thesis topics:, artificial intelligence thesis topics, augmented reality thesis topics, big data analytics thesis topics, bioinformatics thesis topics, blockchain technology thesis topics, cloud computing thesis topics, computer engineering thesis topics, computer vision thesis topics, cybersecurity thesis topics, data science thesis topics, digital transformation thesis topics, distributed systems and networks thesis topics, geographic information systems (gis) thesis topics, human-computer interaction (hci) thesis topics, image processing thesis topics, information system thesis topics, information technology thesis topics.

• Internet Of Things (IoT) Thesis Topics

Machine Learning Thesis Topics

Neural networks thesis topics, programming thesis topics, quantum computing thesis topics, robotics thesis topics, software engineering thesis topics, web development thesis topics.

• Ethical Implications of AI in Decision-Making Processes
• The Role of AI in Personalized Medicine: Opportunities and Challenges
• Advances in AI-Driven Predictive Analytics in Retail
• AI in Autonomous Vehicles: Safety, Regulation, and Technology Integration
• Natural Language Processing: Improving Human-Machine Interaction
• The Future of AI in Cybersecurity: Threats and Defenses
• Machine Learning Algorithms for Real-Time Data Processing
• AI and the Internet of Things: Transforming Smart Home Technology
• The Impact of Deep Learning on Image Recognition Technologies
• Reinforcement Learning: Applications in Robotics and Automation
• AI in Finance: Algorithmic Trading and Risk Assessment
• Bias and Fairness in AI: Addressing Socio-Technical Challenges
• The Evolution of AI in Education: Customized Learning Experiences
• AI for Environmental Conservation: Tracking and Predictive Analysis
• The Role of Artificial Neural Networks in Weather Forecasting
• AI in Agriculture: Predictive Analytics for Crop and Soil Management
• Emotional Recognition AI: Implications for Mental Health Assessments
• AI in Space Exploration: Autonomous Rovers and Mission Planning
• Enhancing User Experience with AI in Video Games
• AI-Powered Virtual Assistants: Trends, Effectiveness, and User Trust
• The Integration of AI in Traditional Industries: Case Studies
• Generative AI Models in Art and Creativity
• AI in LegalTech: Document Analysis and Litigation Prediction
• Healthcare Diagnostics: AI Applications in Radiology and Pathology
• AI and Blockchain: Enhancing Security in Decentralized Systems
• Ethics of AI in Surveillance: Privacy vs. Security
• AI in E-commerce: Personalization Engines and Customer Behavior Analysis
• The Future of AI in Telecommunications: Network Optimization and Service Delivery
• AI in Manufacturing: Predictive Maintenance and Quality Control
• Challenges of AI in Elderly Care: Ethical Considerations and Technological Solutions
• The Role of AI in Public Safety and Emergency Response
• AI for Content Creation: Impact on Media and Journalism
• AI-Driven Algorithms for Efficient Energy Management
• The Role of AI in Cultural Heritage Preservation
• AI and the Future of Public Transport: Optimization and Management
• Enhancing Sports Performance with AI-Based Analytics
• AI in Human Resources: Automating Recruitment and Employee Management
• Real-Time Translation AI: Breaking Language Barriers
• AI in Mental Health: Tools for Monitoring and Therapy Assistance
• The Future of AI Governance: Regulation and Standardization
• AR in Medical Training and Surgery Simulation
• The Impact of Augmented Reality in Retail: Enhancing Consumer Experience
• Augmented Reality for Enhanced Navigation Systems
• AR Applications in Maintenance and Repair in Industrial Settings
• The Role of AR in Enhancing Online Education
• Augmented Reality in Cultural Heritage: Interactive Visitor Experiences
• Developing AR Tools for Improved Sports Coaching and Training
• Privacy and Security Challenges in Augmented Reality Applications
• The Future of AR in Advertising: Engagement and Measurement
• User Interface Design for AR: Principles and Best Practices
• AR in Automotive Industry: Enhancing Driving Experience and Safety
• Augmented Reality for Emergency Response Training
• AR and IoT: Converging Technologies for Smart Environments
• Enhancing Physical Rehabilitation with AR Applications
• The Role of AR in Enhancing Public Safety and Awareness
• Augmented Reality in Fashion: Virtual Fitting and Personalized Shopping
• AR for Environmental Education: Interactive and Immersive Learning
• The Use of AR in Building and Architecture Planning
• AR in the Entertainment Industry: Games and Live Events
• Implementing AR in Museums and Art Galleries for Interactive Learning
• Augmented Reality for Real Estate: Virtual Tours and Property Visualization
• AR in Consumer Electronics: Integration in Smart Devices
• The Development of AR Applications for Children’s Education
• AR for Enhancing User Engagement in Social Media Platforms
• The Application of AR in Field Service Management
• Augmented Reality for Disaster Management and Risk Assessment
• Challenges of Content Creation for Augmented Reality
• Future Trends in AR Hardware: Wearables and Beyond
• Legal and Ethical Considerations of Augmented Reality Technology
• AR in Space Exploration: Tools for Simulation and Training
• Interactive Shopping Experiences with AR: The Future of Retail
• AR in Wildlife Conservation: Educational Tools and Awareness
• The Impact of AR on the Publishing Industry: Interactive Books and Magazines
• Augmented Reality and Its Role in Automotive Manufacturing
• AR for Job Training: Bridging the Skill Gap in Various Industries
• The Role of AR in Therapy: New Frontiers in Mental Health Treatment
• The Future of Augmented Reality in Sports Broadcasting
• AR as a Tool for Enhancing Public Art Installations
• Augmented Reality in the Tourism Industry: Personalized Travel Experiences
• The Use of AR in Security Training: Realistic and Safe Simulations
• The Role of Big Data in Improving Healthcare Outcomes
• Big Data and Its Impact on Consumer Behavior Analysis
• Privacy Concerns in Big Data: Ethical and Legal Implications
• The Application of Big Data in Predictive Maintenance for Manufacturing
• Real-Time Big Data Processing: Tools and Techniques
• Big Data in Financial Services: Fraud Detection and Risk Management
• The Evolution of Big Data Technologies: From Hadoop to Spark
• Big Data Visualization: Techniques for Effective Communication of Insights
• The Integration of Big Data and Artificial Intelligence
• Big Data in Smart Cities: Applications in Traffic Management and Energy Use
• Enhancing Supply Chain Efficiency with Big Data Analytics
• Big Data in Sports Analytics: Improving Team Performance and Fan Engagement
• The Role of Big Data in Environmental Monitoring and Sustainability
• Big Data and Social Media: Analyzing Sentiments and Trends
• Scalability Challenges in Big Data Systems
• The Future of Big Data in Retail: Personalization and Customer Experience
• Big Data in Education: Customized Learning Paths and Student Performance Analysis
• Privacy-Preserving Techniques in Big Data
• Big Data in Public Health: Epidemiology and Disease Surveillance
• The Impact of Big Data on Insurance: Tailored Policies and Pricing
• Edge Computing in Big Data: Processing at the Source
• Big Data and the Internet of Things: Generating Insights from IoT Data
• Cloud-Based Big Data Analytics: Opportunities and Challenges
• Big Data Governance: Policies, Standards, and Management
• The Role of Big Data in Crisis Management and Response
• Machine Learning with Big Data: Building Predictive Models
• Big Data in Agriculture: Precision Farming and Yield Optimization
• The Ethics of Big Data in Research: Consent and Anonymity
• Cross-Domain Big Data Integration: Challenges and Solutions
• Big Data and Cybersecurity: Threat Detection and Prevention Strategies
• Real-Time Streaming Analytics in Big Data
• Big Data in the Media Industry: Content Optimization and Viewer Insights
• The Impact of GDPR on Big Data Practices
• Quantum Computing and Big Data: Future Prospects
• Big Data in E-Commerce: Optimizing Logistics and Inventory Management
• Big Data Talent: Education and Skill Development for Data Scientists
• The Role of Big Data in Political Campaigns and Voting Behavior Analysis
• Big Data and Mental Health: Analyzing Patterns for Better Interventions
• Big Data in Genomics and Personalized Medicine
• The Future of Big Data in Autonomous Driving Technologies
• The Role of Bioinformatics in Personalized Medicine
• Next-Generation Sequencing Data Analysis: Challenges and Opportunities
• Bioinformatics and the Study of Genetic Diseases
• Computational Models for Understanding Protein Structure and Function
• Bioinformatics in Drug Discovery and Development
• The Impact of Big Data on Bioinformatics: Data Management and Analysis
• Machine Learning Applications in Bioinformatics
• Bioinformatics Approaches for Cancer Genomics
• The Development of Bioinformatics Tools for Metagenomics Analysis
• Ethical Considerations in Bioinformatics: Data Sharing and Privacy
• The Role of Bioinformatics in Agricultural Biotechnology
• Bioinformatics and Viral Evolution: Tracking Pathogens and Outbreaks
• The Integration of Bioinformatics and Systems Biology
• Bioinformatics in Neuroscience: Mapping the Brain
• The Future of Bioinformatics in Non-Invasive Prenatal Testing
• Bioinformatics and the Human Microbiome: Health Implications
• The Application of Artificial Intelligence in Bioinformatics
• Structural Bioinformatics: Computational Techniques for Molecular Modeling
• Comparative Genomics: Insights into Evolution and Function
• Bioinformatics in Immunology: Vaccine Design and Immune Response Analysis
• High-Performance Computing in Bioinformatics
• The Challenge of Proteomics in Bioinformatics
• RNA-Seq Data Analysis and Interpretation
• Cloud Computing Solutions for Bioinformatics Data
• Computational Epigenetics: DNA Methylation and Histone Modification Analysis
• Bioinformatics in Ecology: Biodiversity and Conservation Genetics
• The Role of Bioinformatics in Forensic Analysis
• Mobile Apps and Tools for Bioinformatics Research
• Bioinformatics and Public Health: Epidemiological Studies
• The Use of Bioinformatics in Clinical Diagnostics
• Genetic Algorithms in Bioinformatics
• Bioinformatics for Aging Research: Understanding the Mechanisms of Aging
• Data Visualization Techniques in Bioinformatics
• Bioinformatics and the Development of Therapeutic Antibodies
• The Role of Bioinformatics in Stem Cell Research
• Bioinformatics and Cardiovascular Diseases: Genomic Insights
• The Impact of Machine Learning on Functional Genomics in Bioinformatics
• Bioinformatics in Dental Research: Genetic Links to Oral Diseases
• The Future of CRISPR Technology and Bioinformatics
• Bioinformatics and Nutrition: Genomic Insights into Diet and Health
• Blockchain for Enhancing Cybersecurity in Various Industries
• The Impact of Blockchain on Supply Chain Transparency
• Blockchain in Healthcare: Patient Data Management and Security
• The Application of Blockchain in Voting Systems
• Blockchain and Smart Contracts: Legal Implications and Applications
• Cryptocurrencies: Market Trends and the Future of Digital Finance
• Blockchain in Real Estate: Improving Property and Land Registration
• The Role of Blockchain in Managing Digital Identities
• Blockchain for Intellectual Property Management
• Energy Sector Innovations: Blockchain for Renewable Energy Distribution
• Blockchain and the Future of Public Sector Operations
• The Impact of Blockchain on Cross-Border Payments
• Blockchain for Non-Fungible Tokens (NFTs): Applications in Art and Media
• Privacy Issues in Blockchain Applications
• Blockchain in the Automotive Industry: Supply Chain and Beyond
• Decentralized Finance (DeFi): Opportunities and Challenges
• The Role of Blockchain in Combating Counterfeiting and Fraud
• Blockchain for Sustainable Environmental Practices
• The Integration of Artificial Intelligence with Blockchain
• Blockchain Education: Curriculum Development and Training Needs
• Blockchain in the Music Industry: Rights Management and Revenue Distribution
• The Challenges of Blockchain Scalability and Performance Optimization
• The Future of Blockchain in the Telecommunications Industry
• Blockchain and Consumer Data Privacy: A New Paradigm
• Blockchain for Disaster Recovery and Business Continuity
• Blockchain in the Charity and Non-Profit Sectors
• Quantum Resistance in Blockchain: Preparing for the Quantum Era
• Blockchain and Its Impact on Traditional Banking and Financial Institutions
• Legal and Regulatory Challenges Facing Blockchain Technology
• Blockchain for Improved Logistics and Freight Management
• The Role of Blockchain in the Evolution of the Internet of Things (IoT)
• Blockchain and the Future of Gaming: Transparency and Fair Play
• Blockchain for Academic Credentials Verification
• The Application of Blockchain in the Insurance Industry
• Blockchain and the Future of Content Creation and Distribution
• Blockchain for Enhancing Data Integrity in Scientific Research
• The Impact of Blockchain on Human Resources: Employee Verification and Salary Payments
• Blockchain and the Future of Retail: Customer Loyalty Programs and Inventory Management
• Blockchain and Industrial Automation: Trust and Efficiency
• Blockchain for Digital Marketing: Transparency and Consumer Engagement
• Multi-Cloud Strategies: Optimization and Security Challenges
• Advances in Cloud Computing Architectures for Scalable Applications
• Edge Computing: Extending the Reach of Cloud Services
• Cloud Security: Novel Approaches to Data Encryption and Threat Mitigation
• The Impact of Serverless Computing on Software Development Lifecycle
• Cloud Computing and Sustainability: Energy-Efficient Data Centers
• Cloud Service Models: Comparative Analysis of IaaS, PaaS, and SaaS
• Cloud Migration Strategies: Best Practices and Common Pitfalls
• The Role of Cloud Computing in Big Data Analytics
• Implementing AI and Machine Learning Workloads on Cloud Platforms
• Hybrid Cloud Environments: Management Tools and Techniques
• Cloud Computing in Healthcare: Compliance, Security, and Use Cases
• Cost-Effective Cloud Solutions for Small and Medium Enterprises (SMEs)
• The Evolution of Cloud Storage Solutions: Trends and Technologies
• Cloud-Based Disaster Recovery Solutions: Design and Reliability
• Blockchain in Cloud Services: Enhancing Transparency and Trust
• Cloud Networking: Managing Connectivity and Traffic in Cloud Environments
• Cloud Governance: Managing Compliance and Operational Risks
• The Future of Cloud Computing: Quantum Computing Integration
• Performance Benchmarking of Cloud Services Across Different Providers
• Privacy Preservation in Cloud Environments
• Cloud Computing in Education: Virtual Classrooms and Learning Management Systems
• Automation in Cloud Deployments: Tools and Strategies
• Cloud Auditing and Monitoring Techniques
• Mobile Cloud Computing: Challenges and Future Trends
• The Role of Cloud Computing in Digital Media Production and Distribution
• Security Risks in Multi-Tenancy Cloud Environments
• Cloud Computing for Scientific Research: Enabling Complex Simulations
• The Impact of 5G on Cloud Computing Services
• Federated Clouds: Building Collaborative Cloud Environments
• Managing Software Dependencies in Cloud Applications
• The Economics of Cloud Computing: Cost Models and Pricing Strategies
• Cloud Computing in Government: Security Protocols and Citizen Services
• Cloud Access Security Brokers (CASBs): Security Enforcement Points
• DevOps in the Cloud: Strategies for Continuous Integration and Deployment
• Predictive Analytics in Cloud Computing
• The Role of Cloud Computing in IoT Deployment
• Implementing Robust Cybersecurity Measures in Cloud Architecture
• Cloud Computing in the Financial Sector: Handling Sensitive Data
• Future Trends in Cloud Computing: The Role of AI in Cloud Optimization
• Advances in Microprocessor Design and Architecture
• FPGA-Based Design: Innovations and Applications
• The Role of Embedded Systems in Consumer Electronics
• Quantum Computing: Hardware Development and Challenges
• High-Performance Computing (HPC) and Parallel Processing
• Design and Analysis of Computer Networks
• Cyber-Physical Systems: Design, Analysis, and Security
• The Impact of Nanotechnology on Computer Hardware
• Wireless Sensor Networks: Design and Optimization
• Cryptographic Hardware: Implementations and Security Evaluations
• Machine Learning Techniques for Hardware Optimization
• Hardware for Artificial Intelligence: GPUs vs. TPUs
• Energy-Efficient Hardware Designs for Sustainable Computing
• Security Aspects of Mobile and Ubiquitous Computing
• Advanced Algorithms for Computer-Aided Design (CAD) of VLSI
• Signal Processing in Communication Systems
• The Development of Wearable Computing Devices
• Computer Hardware Testing: Techniques and Tools
• The Role of Hardware in Network Security
• The Evolution of Interface Designs in Consumer Electronics
• Biometric Systems: Hardware and Software Integration
• The Integration of IoT Devices in Smart Environments
• Electronic Design Automation (EDA) Tools and Methodologies
• Robotics: Hardware Design and Control Systems
• Hardware Accelerators for Deep Learning Applications
• Developments in Non-Volatile Memory Technologies
• The Future of Computer Hardware in the Era of Quantum Computing
• Hardware Solutions for Data Storage and Retrieval
• Power Management Techniques in Embedded Systems
• Challenges in Designing Multi-Core Processors
• System on Chip (SoC) Design Trends and Challenges
• The Role of Computer Engineering in Aerospace Technology
• Real-Time Systems: Design and Implementation Challenges
• Hardware Support for Virtualization Technology
• Advances in Computer Graphics Hardware
• The Impact of 5G Technology on Mobile Computing Hardware
• Environmental Impact Assessment of Computer Hardware Production
• Security Vulnerabilities in Modern Microprocessors
• Computer Hardware Innovations in the Automotive Industry
• The Role of Computer Engineering in Medical Device Technology
• Deep Learning Approaches to Object Recognition
• Real-Time Image Processing for Autonomous Vehicles
• Computer Vision in Robotic Surgery: Techniques and Challenges
• Facial Recognition Technology: Innovations and Privacy Concerns
• Machine Vision in Industrial Automation and Quality Control
• 3D Reconstruction Techniques in Computer Vision
• Enhancing Sports Analytics with Computer Vision
• Augmented Reality: Integrating Computer Vision for Immersive Experiences
• Computer Vision for Environmental Monitoring
• Thermal Imaging and Its Applications in Computer Vision
• Computer Vision in Retail: Customer Behavior and Store Layout Optimization
• Motion Detection and Tracking in Security Systems
• The Role of Computer Vision in Content Moderation on Social Media
• Gesture Recognition: Methods and Applications
• Computer Vision in Agriculture: Pest Detection and Crop Analysis
• Advances in Medical Imaging: Machine Learning and Computer Vision
• Scene Understanding and Contextual Inference in Images
• The Development of Vision-Based Autonomous Drones
• Optical Character Recognition (OCR): Latest Techniques and Applications
• The Impact of Computer Vision on Virtual Reality Experiences
• Biometrics: Enhancing Security Systems with Computer Vision
• Computer Vision for Wildlife Conservation: Species Recognition and Behavior Analysis
• Underwater Image Processing: Challenges and Techniques
• Video Surveillance: The Evolution of Algorithmic Approaches
• Advanced Driver-Assistance Systems (ADAS): Leveraging Computer Vision
• Computational Photography: Enhancing Image Capture Techniques
• The Integration of AI in Computer Vision: Ethical and Technical Considerations
• Computer Vision in the Gaming Industry: From Design to Interaction
• The Future of Computer Vision in Smart Cities
• Pattern Recognition in Historical Document Analysis
• The Role of Computer Vision in the Manufacturing of Customized Products
• Enhancing Accessibility with Computer Vision: Tools for the Visually Impaired
• The Use of Computer Vision in Behavioral Research
• Predictive Analytics with Computer Vision in Sports
• Image Synthesis with Generative Adversarial Networks (GANs)
• The Use of Computer Vision in Remote Sensing
• Real-Time Video Analytics for Public Safety
• The Role of Computer Vision in Telemedicine
• Computer Vision and the Internet of Things (IoT): A Synergistic Approach
• Future Trends in Computer Vision: Quantum Computing and Beyond
• Advances in Cryptography: Post-Quantum Cryptosystems
• Artificial Intelligence in Cybersecurity: Threat Detection and Response
• Blockchain for Enhanced Security in Distributed Networks
• The Impact of IoT on Cybersecurity: Vulnerabilities and Solutions
• Cybersecurity in Cloud Computing: Best Practices and Tools
• Ethical Hacking: Techniques and Ethical Implications
• The Role of Human Factors in Cybersecurity Breaches
• Privacy-preserving Technologies in an Age of Surveillance
• The Evolution of Ransomware Attacks and Defense Strategies
• Secure Software Development: Integrating Security in DevOps (DevSecOps)
• Cybersecurity in Critical Infrastructure: Challenges and Innovations
• The Future of Biometric Security Systems
• Cyber Warfare: State-sponsored Attacks and Defense Mechanisms
• The Role of Cybersecurity in Protecting Digital Identities
• Social Engineering Attacks: Prevention and Countermeasures
• Mobile Security: Protecting Against Malware and Exploits
• Wireless Network Security: Protocols and Practices
• Data Breaches: Analysis, Consequences, and Mitigation
• The Ethics of Cybersecurity: Balancing Privacy and Security
• Regulatory Compliance and Cybersecurity: GDPR and Beyond
• The Impact of 5G Technology on Cybersecurity
• The Role of Machine Learning in Cyber Threat Intelligence
• Cybersecurity in Automotive Systems: Challenges in a Connected Environment
• The Use of Virtual Reality for Cybersecurity Training and Simulation
• Advanced Persistent Threats (APT): Detection and Response
• Cybersecurity for Smart Cities: Challenges and Solutions
• Deep Learning Applications in Malware Detection
• The Role of Cybersecurity in Healthcare: Protecting Patient Data
• Supply Chain Cybersecurity: Identifying Risks and Solutions
• Endpoint Security: Trends, Challenges, and Future Directions
• Forensic Techniques in Cybersecurity: Tracking and Analyzing Cyber Crimes
• The Influence of International Law on Cyber Operations
• Protecting Financial Institutions from Cyber Frauds and Attacks
• Quantum Computing and Its Implications for Cybersecurity
• Cybersecurity and Remote Work: Emerging Threats and Strategies
• IoT Security in Industrial Applications
• Cyber Insurance: Risk Assessment and Management
• Security Challenges in Edge Computing Environments
• Anomaly Detection in Network Security Using AI Techniques
• Securing the Software Supply Chain in Application Development
• Big Data Analytics: Techniques and Applications in Real-time
• Machine Learning Algorithms for Predictive Analytics
• Data Science in Healthcare: Improving Patient Outcomes with Predictive Models
• The Role of Data Science in Financial Market Predictions
• Natural Language Processing: Emerging Trends and Applications
• Data Visualization Tools and Techniques for Enhanced Business Intelligence
• Ethics in Data Science: Privacy, Fairness, and Transparency
• The Use of Data Science in Environmental Science for Sustainability Studies
• The Impact of Data Science on Social Media Marketing Strategies
• Data Mining Techniques for Detecting Patterns in Large Datasets
• AI and Data Science: Synergies and Future Prospects
• Reinforcement Learning: Applications and Challenges in Data Science
• The Role of Data Science in E-commerce Personalization
• Predictive Maintenance in Manufacturing Through Data Science
• The Evolution of Recommendation Systems in Streaming Services
• Real-time Data Processing with Stream Analytics
• Deep Learning for Image and Video Analysis
• Data Governance in Big Data Analytics
• Text Analytics and Sentiment Analysis for Customer Feedback
• Fraud Detection in Banking and Insurance Using Data Science
• The Integration of IoT Data in Data Science Models
• The Future of Data Science in Quantum Computing
• Data Science for Public Health: Epidemic Outbreak Prediction
• Sports Analytics: Performance Improvement and Injury Prevention
• Data Science in Retail: Inventory Management and Customer Journey Analysis
• Data Science in Smart Cities: Traffic and Urban Planning
• The Use of Blockchain in Data Security and Integrity
• Geospatial Analysis for Environmental Monitoring
• Time Series Analysis in Economic Forecasting
• Data Science in Education: Analyzing Trends and Student Performance
• Predictive Policing: Data Science in Law Enforcement
• Data Science in Agriculture: Yield Prediction and Soil Health
• Computational Social Science: Analyzing Societal Trends
• Data Science in Energy Sector: Consumption and Optimization
• Personalization Technologies in Healthcare Through Data Science
• The Role of Data Science in Content Creation and Media
• Anomaly Detection in Network Security Using Data Science Techniques
• The Future of Autonomous Vehicles: Data Science-Driven Innovations
• Multimodal Data Fusion Techniques in Data Science
• Scalability Challenges in Data Science Projects
• The Role of Digital Transformation in Business Model Innovation
• The Impact of Digital Technologies on Customer Experience
• Digital Transformation in the Banking Sector: Trends and Challenges
• The Use of AI and Robotics in Digital Transformation of Manufacturing
• Digital Transformation in Healthcare: Telemedicine and Beyond
• The Influence of Big Data on Decision-Making Processes in Corporations
• Blockchain as a Driver for Transparency in Digital Transformation
• The Role of IoT in Enhancing Operational Efficiency in Industries
• Digital Marketing Strategies: SEO, Content, and Social Media
• The Integration of Cyber-Physical Systems in Industrial Automation
• Digital Transformation in Education: Virtual Learning Environments
• Smart Cities: The Role of Digital Technologies in Urban Planning
• Digital Transformation in the Retail Sector: E-commerce Evolution
• The Future of Work: Impact of Digital Transformation on Workplaces
• Cybersecurity Challenges in a Digitally Transformed World
• Mobile Technologies and Their Impact on Digital Transformation
• The Role of Digital Twin Technology in Industry 4.0
• Digital Transformation in the Public Sector: E-Government Services
• Data Privacy and Security in the Age of Digital Transformation
• Digital Transformation in the Energy Sector: Smart Grids and Renewable Energy
• The Use of Augmented Reality in Training and Development
• The Role of Virtual Reality in Real Estate and Architecture
• Digital Transformation and Sustainability: Reducing Environmental Footprint
• The Role of Digital Transformation in Supply Chain Optimization
• Digital Transformation in Agriculture: IoT and Smart Farming
• The Impact of 5G on Digital Transformation Initiatives
• The Influence of Digital Transformation on Media and Entertainment
• Digital Transformation in Insurance: Telematics and Risk Assessment
• The Role of AI in Enhancing Customer Service Operations
• The Future of Digital Transformation: Trends and Predictions
• Digital Transformation and Corporate Governance
• The Role of Leadership in Driving Digital Transformation
• Digital Transformation in Non-Profit Organizations: Challenges and Benefits
• The Economic Implications of Digital Transformation
• The Cultural Impact of Digital Transformation on Organizations
• Digital Transformation in Transportation: Logistics and Fleet Management
• User Experience (UX) Design in Digital Transformation
• The Role of Digital Transformation in Crisis Management
• Digital Transformation and Human Resource Management
• Implementing Change Management in Digital Transformation Projects
• Scalability Challenges in Distributed Systems: Solutions and Strategies
• Blockchain Technology: Enhancing Security and Transparency in Distributed Networks
• The Role of Edge Computing in Distributed Systems
• Designing Fault-Tolerant Systems in Distributed Networks
• The Impact of 5G Technology on Distributed Network Architectures
• Machine Learning Algorithms for Network Traffic Analysis
• Load Balancing Techniques in Distributed Computing
• The Use of Distributed Ledger Technology Beyond Cryptocurrencies
• Network Function Virtualization (NFV) and Its Impact on Service Providers
• The Evolution of Software-Defined Networking (SDN) in Enterprise Environments
• Implementing Robust Cybersecurity Measures in Distributed Systems
• Quantum Computing: Implications for Network Security in Distributed Systems
• Peer-to-Peer Network Protocols and Their Applications
• The Internet of Things (IoT): Network Challenges and Communication Protocols
• Real-Time Data Processing in Distributed Sensor Networks
• The Role of Artificial Intelligence in Optimizing Network Operations
• Privacy and Data Protection Strategies in Distributed Systems
• The Future of Distributed Computing in Cloud Environments
• Energy Efficiency in Distributed Network Systems
• Wireless Mesh Networks: Design, Challenges, and Applications
• Multi-Access Edge Computing (MEC): Use Cases and Deployment Challenges
• Consensus Algorithms in Distributed Systems: From Blockchain to New Applications
• The Use of Containers and Microservices in Building Scalable Applications
• Network Slicing for 5G: Opportunities and Challenges
• The Role of Distributed Systems in Big Data Analytics
• Managing Data Consistency in Distributed Databases
• The Impact of Distributed Systems on Digital Transformation Strategies
• Augmented Reality over Distributed Networks: Performance and Scalability Issues
• The Application of Distributed Systems in Smart Grid Technology
• Developing Distributed Applications Using Serverless Architectures
• The Challenges of Implementing IPv6 in Distributed Networks
• Distributed Systems for Disaster Recovery: Design and Implementation
• The Use of Virtual Reality in Distributed Network Environments
• Security Protocols for Ad Hoc Networks in Emergency Situations
• The Role of Distributed Networks in Enhancing Mobile Broadband Services
• Next-Generation Protocols for Enhanced Network Reliability and Performance
• The Application of Blockchain in Securing Distributed IoT Networks
• Dynamic Resource Allocation Strategies in Distributed Systems
• The Integration of Distributed Systems with Existing IT Infrastructure
• The Future of Autonomous Systems in Distributed Networking
• The Integration of GIS with Remote Sensing for Environmental Monitoring
• GIS in Urban Planning: Techniques for Sustainable Development
• The Role of GIS in Disaster Management and Response Strategies
• Real-Time GIS Applications in Traffic Management and Route Planning
• The Use of GIS in Water Resource Management
• GIS and Public Health: Tracking Epidemics and Healthcare Access
• Advances in 3D GIS: Technologies and Applications
• GIS in Agricultural Management: Precision Farming Techniques
• The Impact of GIS on Biodiversity Conservation Efforts
• Spatial Data Analysis for Crime Pattern Detection and Prevention
• GIS in Renewable Energy: Site Selection and Resource Management
• The Role of GIS in Historical Research and Archaeology
• GIS and Machine Learning: Integrating Spatial Analysis with Predictive Models
• Cloud Computing and GIS: Enhancing Accessibility and Data Processing
• The Application of GIS in Managing Public Transportation Systems
• GIS in Real Estate: Market Analysis and Property Valuation
• The Use of GIS for Environmental Impact Assessments
• Mobile GIS Applications: Development and Usage Trends
• GIS and Its Role in Smart City Initiatives
• Privacy Issues in the Use of Geographic Information Systems
• GIS in Forest Management: Monitoring and Conservation Strategies
• The Impact of GIS on Tourism: Enhancing Visitor Experiences through Technology
• GIS in the Insurance Industry: Risk Assessment and Policy Design
• The Development of Participatory GIS (PGIS) for Community Engagement
• GIS in Coastal Management: Addressing Erosion and Flood Risks
• Geospatial Analytics in Retail: Optimizing Location and Consumer Insights
• GIS for Wildlife Tracking and Habitat Analysis
• The Use of GIS in Climate Change Studies
• GIS and Social Media: Analyzing Spatial Trends from User Data
• The Future of GIS: Augmented Reality and Virtual Reality Applications
• GIS in Education: Tools for Teaching Geographic Concepts
• The Role of GIS in Land Use Planning and Zoning
• GIS for Emergency Medical Services: Optimizing Response Times
• Open Source GIS Software: Development and Community Contributions
• GIS and the Internet of Things (IoT): Converging Technologies for Advanced Monitoring
• GIS for Mineral Exploration: Techniques and Applications
• The Role of GIS in Municipal Management and Services
• GIS and Drone Technology: A Synergy for Precision Mapping
• Spatial Statistics in GIS: Techniques for Advanced Data Analysis
• Future Trends in GIS: The Integration of AI for Smarter Solutions
• The Evolution of User Interface (UI) Design: From Desktop to Mobile and Beyond
• The Role of HCI in Enhancing Accessibility for Disabled Users
• Virtual Reality (VR) and Augmented Reality (AR) in HCI: New Dimensions of Interaction
• The Impact of HCI on User Experience (UX) in Software Applications
• Cognitive Aspects of HCI: Understanding User Perception and Behavior
• HCI and the Internet of Things (IoT): Designing Interactive Smart Devices
• The Use of Biometrics in HCI: Security and Usability Concerns
• HCI in Educational Technologies: Enhancing Learning through Interaction
• Emotional Recognition and Its Application in HCI
• The Role of HCI in Wearable Technology: Design and Functionality
• Advanced Techniques in Voice User Interfaces (VUIs)
• The Impact of HCI on Social Media Interaction Patterns
• HCI in Healthcare: Designing User-Friendly Medical Devices and Software
• HCI and Gaming: Enhancing Player Engagement and Experience
• The Use of HCI in Robotic Systems: Improving Human-Robot Interaction
• The Influence of HCI on E-commerce: Optimizing User Journeys and Conversions
• HCI in Smart Homes: Interaction Design for Automated Environments
• Multimodal Interaction: Integrating Touch, Voice, and Gesture in HCI
• HCI and Aging: Designing Technology for Older Adults
• The Role of HCI in Virtual Teams: Tools and Strategies for Collaboration
• User-Centered Design: HCI Strategies for Developing User-Focused Software
• HCI Research Methodologies: Experimental Design and User Studies
• The Application of HCI Principles in the Design of Public Kiosks
• The Future of HCI: Integrating Artificial Intelligence for Smarter Interfaces
• HCI in Transportation: Designing User Interfaces for Autonomous Vehicles
• Privacy and Ethics in HCI: Addressing User Data Security
• HCI and Environmental Sustainability: Promoting Eco-Friendly Behaviors
• Adaptive Interfaces: HCI Design for Personalized User Experiences
• The Role of HCI in Content Creation: Tools for Artists and Designers
• HCI for Crisis Management: Designing Systems for Emergency Use
• The Use of HCI in Sports Technology: Enhancing Training and Performance
• The Evolution of Haptic Feedback in HCI
• HCI and Cultural Differences: Designing for Global User Bases
• The Impact of HCI on Digital Marketing: Creating Engaging User Interactions
• HCI in Financial Services: Improving User Interfaces for Banking Apps
• The Role of HCI in Enhancing User Trust in Technology
• HCI for Public Safety: User Interfaces for Security Systems
• The Application of HCI in the Film and Television Industry
• HCI and the Future of Work: Designing Interfaces for Remote Collaboration
• Innovations in HCI: Exploring New Interaction Technologies and Their Applications
• Deep Learning Techniques for Advanced Image Segmentation
• Real-Time Image Processing for Autonomous Driving Systems
• Image Enhancement Algorithms for Underwater Imaging
• Super-Resolution Imaging: Techniques and Applications
• The Role of Image Processing in Remote Sensing and Satellite Imagery Analysis
• Machine Learning Models for Medical Image Diagnosis
• The Impact of AI on Photographic Restoration and Enhancement
• Image Processing in Security Systems: Facial Recognition and Motion Detection
• Advanced Algorithms for Image Noise Reduction
• 3D Image Reconstruction Techniques in Tomography
• Image Processing for Agricultural Monitoring: Crop Disease Detection and Yield Prediction
• Techniques for Panoramic Image Stitching
• Video Image Processing: Real-Time Streaming and Data Compression
• The Application of Image Processing in Printing Technology
• Color Image Processing: Theory and Practical Applications
• The Use of Image Processing in Biometrics Identification
• Computational Photography: Image Processing Techniques in Smartphone Cameras
• Image Processing for Augmented Reality: Real-time Object Overlay
• The Development of Image Processing Algorithms for Traffic Control Systems
• Pattern Recognition and Analysis in Forensic Imaging
• Adaptive Filtering Techniques in Image Processing
• Image Processing in Retail: Customer Tracking and Behavior Analysis
• The Role of Image Processing in Cultural Heritage Preservation
• Image Segmentation Techniques for Cancer Detection in Medical Imaging
• High Dynamic Range (HDR) Imaging: Algorithms and Display Techniques
• Image Classification with Deep Convolutional Neural Networks
• The Evolution of Edge Detection Algorithms in Image Processing
• Image Processing for Wildlife Monitoring: Species Recognition and Behavior Analysis
• Application of Wavelet Transforms in Image Compression
• Image Processing in Sports: Enhancing Broadcasts and Performance Analysis
• Optical Character Recognition (OCR) Improvements in Document Scanning
• Multi-Spectral Imaging for Environmental and Earth Studies
• Image Processing for Space Exploration: Analysis of Planetary Images
• Real-Time Image Processing for Event Surveillance
• The Influence of Quantum Computing on Image Processing Speed and Security
• Machine Vision in Manufacturing: Defect Detection and Quality Control
• Image Processing in Neurology: Visualizing Brain Functions
• Photogrammetry and Image Processing in Geology: 3D Terrain Mapping
• Advanced Techniques in Image Watermarking for Copyright Protection
• The Future of Image Processing: Integrating AI for Automated Editing
• The Evolution of Enterprise Resource Planning (ERP) Systems in the Digital Age
• Information Systems for Managing Distributed Workforces
• The Role of Information Systems in Enhancing Supply Chain Management
• Cybersecurity Measures in Information Systems
• The Impact of Big Data on Decision Support Systems
• Blockchain Technology for Information System Security
• The Development of Sustainable IT Infrastructure in Information Systems
• The Use of AI in Information Systems for Business Intelligence
• Information Systems in Healthcare: Improving Patient Care and Data Management
• The Influence of IoT on Information Systems Architecture
• Mobile Information Systems: Development and Usability Challenges
• The Role of Geographic Information Systems (GIS) in Urban Planning
• Social Media Analytics: Tools and Techniques in Information Systems
• Information Systems in Education: Enhancing Learning and Administration
• Cloud Computing Integration into Corporate Information Systems
• Information Systems Audit: Practices and Challenges
• User Interface Design and User Experience in Information Systems
• Privacy and Data Protection in Information Systems
• The Future of Quantum Computing in Information Systems
• The Role of Information Systems in Environmental Management
• Implementing Effective Knowledge Management Systems
• The Adoption of Virtual Reality in Information Systems
• The Challenges of Implementing ERP Systems in Multinational Corporations
• Information Systems for Real-Time Business Analytics
• The Impact of 5G Technology on Mobile Information Systems
• Ethical Issues in the Management of Information Systems
• Information Systems in Retail: Enhancing Customer Experience and Management
• The Role of Information Systems in Non-Profit Organizations
• Development of Decision Support Systems for Strategic Planning
• Information Systems in the Banking Sector: Enhancing Financial Services
• Risk Management in Information Systems
• The Integration of Artificial Neural Networks in Information Systems
• Information Systems and Corporate Governance
• Information Systems for Disaster Response and Management
• The Role of Information Systems in Sports Management
• Information Systems for Public Health Surveillance
• The Future of Information Systems: Trends and Predictions
• Information Systems in the Film and Media Industry
• Business Process Reengineering through Information Systems
• Implementing Customer Relationship Management (CRM) Systems in E-commerce
• Emerging Trends in Artificial Intelligence and Machine Learning
• The Future of Cloud Services and Technology
• Cybersecurity: Current Threats and Future Defenses
• The Role of Information Technology in Sustainable Energy Solutions
• Internet of Things (IoT): From Smart Homes to Smart Cities
• Blockchain and Its Impact on Information Technology
• The Use of Big Data Analytics in Predictive Modeling
• Virtual Reality (VR) and Augmented Reality (AR): The Next Frontier in IT
• The Challenges of Digital Transformation in Traditional Businesses
• Wearable Technology: Health Monitoring and Beyond
• 5G Technology: Implementation and Impacts on IT
• Biometrics Technology: Uses and Privacy Concerns
• The Role of IT in Global Health Initiatives
• Ethical Considerations in the Development of Autonomous Systems
• Data Privacy in the Age of Information Overload
• The Evolution of Software Development Methodologies
• Quantum Computing: The Next Revolution in IT
• IT Governance: Best Practices and Standards
• The Integration of AI in Customer Service Technology
• IT in Manufacturing: Industrial Automation and Robotics
• The Future of E-commerce: Technology and Trends
• Mobile Computing: Innovations and Challenges
• Information Technology in Education: Tools and Trends
• IT Project Management: Approaches and Tools
• The Role of IT in Media and Entertainment
• The Impact of Digital Marketing Technologies on Business Strategies
• IT in Logistics and Supply Chain Management
• The Development and Future of Autonomous Vehicles
• IT in the Insurance Sector: Enhancing Efficiency and Customer Engagement
• The Role of IT in Environmental Conservation
• Smart Grid Technology: IT at the Intersection of Energy Management
• Telemedicine: The Impact of IT on Healthcare Delivery
• IT in the Agricultural Sector: Innovations and Impact
• Cyber-Physical Systems: IT in the Integration of Physical and Digital Worlds
• The Influence of Social Media Platforms on IT Development
• Data Centers: Evolution, Technologies, and Sustainability
• IT in Public Administration: Improving Services and Transparency
• The Role of IT in Sports Analytics
• Information Technology in Retail: Enhancing the Shopping Experience
• The Future of IT: Integrating Ethical AI Systems

Internet of Things (IoT) Thesis Topics

• Enhancing IoT Security: Strategies for Safeguarding Connected Devices
• IoT in Smart Cities: Infrastructure and Data Management Challenges
• The Application of IoT in Precision Agriculture: Maximizing Efficiency and Yield
• IoT and Healthcare: Opportunities for Remote Monitoring and Patient Care
• Energy Efficiency in IoT: Techniques for Reducing Power Consumption in Devices
• The Role of IoT in Supply Chain Management and Logistics
• Real-Time Data Processing Using Edge Computing in IoT Networks
• Privacy Concerns and Data Protection in IoT Systems
• The Integration of IoT with Blockchain for Enhanced Security and Transparency
• IoT in Environmental Monitoring: Systems for Air Quality and Water Safety
• Predictive Maintenance in Industrial IoT: Strategies and Benefits
• IoT in Retail: Enhancing Customer Experience through Smart Technology
• The Development of Standard Protocols for IoT Communication
• IoT in Smart Homes: Automation and Security Systems
• The Role of IoT in Disaster Management: Early Warning Systems and Response Coordination
• Machine Learning Techniques for IoT Data Analytics
• IoT in Automotive: The Future of Connected and Autonomous Vehicles
• The Impact of 5G on IoT: Enhancements in Speed and Connectivity
• IoT Device Lifecycle Management: From Creation to Decommissioning
• IoT in Public Safety: Applications for Emergency Response and Crime Prevention
• The Ethics of IoT: Balancing Innovation with Consumer Rights
• IoT and the Future of Work: Automation and Labor Market Shifts
• Designing User-Friendly Interfaces for IoT Applications
• IoT in the Energy Sector: Smart Grids and Renewable Energy Integration
• Quantum Computing and IoT: Potential Impacts and Applications
• The Role of AI in Enhancing IoT Solutions
• IoT for Elderly Care: Technologies for Health and Mobility Assistance
• IoT in Education: Enhancing Classroom Experiences and Learning Outcomes
• Challenges in Scaling IoT Infrastructure for Global Coverage
• The Economic Impact of IoT: Industry Transformations and New Business Models
• IoT and Tourism: Enhancing Visitor Experiences through Connected Technologies
• Data Fusion Techniques in IoT: Integrating Diverse Data Sources
• IoT in Aquaculture: Monitoring and Managing Aquatic Environments
• Wireless Technologies for IoT: Comparing LoRa, Zigbee, and NB-IoT
• IoT and Intellectual Property: Navigating the Legal Landscape
• IoT in Sports: Enhancing Training and Audience Engagement
• Building Resilient IoT Systems against Cyber Attacks
• IoT for Waste Management: Innovations and System Implementations
• IoT in Agriculture: Drones and Sensors for Crop Monitoring
• The Role of IoT in Cultural Heritage Preservation: Monitoring and Maintenance
• Advanced Algorithms for Supervised and Unsupervised Learning
• Machine Learning in Genomics: Predicting Disease Propensity and Treatment Outcomes
• The Use of Neural Networks in Image Recognition and Analysis
• Reinforcement Learning: Applications in Robotics and Autonomous Systems
• The Role of Machine Learning in Natural Language Processing and Linguistic Analysis
• Deep Learning for Predictive Analytics in Business and Finance
• Machine Learning for Cybersecurity: Detection of Anomalies and Malware
• Ethical Considerations in Machine Learning: Bias and Fairness
• The Integration of Machine Learning with IoT for Smart Device Management
• Transfer Learning: Techniques and Applications in New Domains
• The Application of Machine Learning in Environmental Science
• Machine Learning in Healthcare: Diagnosing Conditions from Medical Images
• The Use of Machine Learning in Algorithmic Trading and Stock Market Analysis
• Machine Learning in Social Media: Sentiment Analysis and Trend Prediction
• Quantum Machine Learning: Merging Quantum Computing with AI
• Feature Engineering and Selection in Machine Learning
• Machine Learning for Enhancing User Experience in Mobile Applications
• The Impact of Machine Learning on Digital Marketing Strategies
• Machine Learning for Energy Consumption Forecasting and Optimization
• The Role of Machine Learning in Enhancing Network Security Protocols
• Scalability and Efficiency of Machine Learning Algorithms
• Machine Learning in Drug Discovery and Pharmaceutical Research
• The Application of Machine Learning in Sports Analytics
• Machine Learning for Real-Time Decision-Making in Autonomous Vehicles
• The Use of Machine Learning in Predicting Geographical and Meteorological Events
• Machine Learning for Educational Data Mining and Learning Analytics
• The Role of Machine Learning in Audio Signal Processing
• Predictive Maintenance in Manufacturing Through Machine Learning
• Machine Learning and Its Implications for Privacy and Surveillance
• The Application of Machine Learning in Augmented Reality Systems
• Deep Learning Techniques in Medical Diagnosis: Challenges and Opportunities
• The Use of Machine Learning in Video Game Development
• Machine Learning for Fraud Detection in Financial Services
• The Role of Machine Learning in Agricultural Optimization and Management
• The Impact of Machine Learning on Content Personalization and Recommendation Systems
• Machine Learning in Legal Tech: Document Analysis and Case Prediction
• Adaptive Learning Systems: Tailoring Education Through Machine Learning
• Machine Learning in Space Exploration: Analyzing Data from Space Missions
• Machine Learning for Public Sector Applications: Improving Services and Efficiency
• The Future of Machine Learning: Integrating Explainable AI
• Innovations in Convolutional Neural Networks for Image and Video Analysis
• Recurrent Neural Networks: Applications in Sequence Prediction and Analysis
• The Role of Neural Networks in Predicting Financial Market Trends
• Deep Neural Networks for Enhanced Speech Recognition Systems
• Neural Networks in Medical Imaging: From Detection to Diagnosis
• Generative Adversarial Networks (GANs): Applications in Art and Media
• The Use of Neural Networks in Autonomous Driving Technologies
• Neural Networks for Real-Time Language Translation
• The Application of Neural Networks in Robotics: Sensory Data and Movement Control
• Neural Network Optimization Techniques: Overcoming Overfitting and Underfitting
• The Integration of Neural Networks with Blockchain for Data Security
• Neural Networks in Climate Modeling and Weather Forecasting
• The Use of Neural Networks in Enhancing Internet of Things (IoT) Devices
• Graph Neural Networks: Applications in Social Network Analysis and Beyond
• The Impact of Neural Networks on Augmented Reality Experiences
• Neural Networks for Anomaly Detection in Network Security
• The Application of Neural Networks in Bioinformatics and Genomic Data Analysis
• Capsule Neural Networks: Improving the Robustness and Interpretability of Deep Learning
• The Role of Neural Networks in Consumer Behavior Analysis
• Neural Networks in Energy Sector: Forecasting and Optimization
• The Evolution of Neural Network Architectures for Efficient Learning
• The Use of Neural Networks in Sentiment Analysis: Techniques and Challenges
• Deep Reinforcement Learning: Strategies for Advanced Decision-Making Systems
• Neural Networks for Precision Medicine: Tailoring Treatments to Individual Genetic Profiles
• The Use of Neural Networks in Virtual Assistants: Enhancing Natural Language Understanding
• The Impact of Neural Networks on Pharmaceutical Research
• Neural Networks for Supply Chain Management: Prediction and Automation
• The Application of Neural Networks in E-commerce: Personalization and Recommendation Systems
• Neural Networks for Facial Recognition: Advances and Ethical Considerations
• The Role of Neural Networks in Educational Technologies
• The Use of Neural Networks in Predicting Economic Trends
• Neural Networks in Sports: Analyzing Performance and Strategy
• The Impact of Neural Networks on Digital Security Systems
• Neural Networks for Real-Time Video Surveillance Analysis
• The Integration of Neural Networks in Edge Computing Devices
• Neural Networks for Industrial Automation: Improving Efficiency and Accuracy
• The Future of Neural Networks: Towards More General AI Applications
• Neural Networks in Art and Design: Creating New Forms of Expression
• The Role of Neural Networks in Enhancing Public Health Initiatives
• The Future of Neural Networks: Challenges in Scalability and Generalization
• The Evolution of Programming Paradigms: Functional vs. Object-Oriented Programming
• Advances in Compiler Design and Optimization Techniques
• The Impact of Programming Languages on Software Security
• Developing Programming Languages for Quantum Computing
• Machine Learning in Automated Code Generation and Optimization
• The Role of Programming in Developing Scalable Cloud Applications
• The Future of Web Development: New Frameworks and Technologies
• Cross-Platform Development: Best Practices in Mobile App Programming
• The Influence of Programming Techniques on Big Data Analytics
• Real-Time Systems Programming: Challenges and Solutions
• The Integration of Programming with Blockchain Technology
• Programming for IoT: Languages and Tools for Device Communication
• Secure Coding Practices: Preventing Cyber Attacks through Software Design
• The Role of Programming in Data Visualization and User Interface Design
• Advances in Game Programming: Graphics, AI, and Network Play
• The Impact of Programming on Digital Media and Content Creation
• Programming Languages for Robotics: Trends and Future Directions
• The Use of Artificial Intelligence in Enhancing Programming Productivity
• Programming for Augmented and Virtual Reality: New Challenges and Techniques
• Ethical Considerations in Programming: Bias, Fairness, and Transparency
• The Future of Programming Education: Interactive and Adaptive Learning Models
• Programming for Wearable Technology: Special Considerations and Challenges
• The Evolution of Programming in Financial Technology
• Functional Programming in Enterprise Applications
• Memory Management Techniques in Programming: From Garbage Collection to Manual Control
• The Role of Open Source Programming in Accelerating Innovation
• The Impact of Programming on Network Security and Cryptography
• Developing Accessible Software: Programming for Users with Disabilities
• Programming Language Theories: New Models and Approaches
• The Challenges of Legacy Code: Strategies for Modernization and Integration
• Energy-Efficient Programming: Optimizing Code for Green Computing
• Multithreading and Concurrency: Advanced Programming Techniques
• The Impact of Programming on Computational Biology and Bioinformatics
• The Role of Scripting Languages in Automating System Administration
• Programming and the Future of Quantum Resistant Cryptography
• Code Review and Quality Assurance: Techniques and Tools
• Adaptive and Predictive Programming for Dynamic Environments
• The Role of Programming in Enhancing E-commerce Technology
• Programming for Cyber-Physical Systems: Bridging the Gap Between Digital and Physical
• The Influence of Programming Languages on Computational Efficiency and Performance
• Quantum Algorithms: Development and Applications Beyond Shor’s and Grover’s Algorithms
• The Role of Quantum Computing in Solving Complex Biological Problems
• Quantum Cryptography: New Paradigms for Secure Communication
• Error Correction Techniques in Quantum Computing
• Quantum Computing and Its Impact on Artificial Intelligence
• The Integration of Classical and Quantum Computing: Hybrid Models
• Quantum Machine Learning: Theoretical Foundations and Practical Applications
• Quantum Computing Hardware: Advances in Qubit Technology
• The Application of Quantum Computing in Financial Modeling and Risk Assessment
• Quantum Networking: Establishing Secure Quantum Communication Channels
• The Future of Drug Discovery: Applications of Quantum Computing
• Quantum Computing in Cryptanalysis: Threats to Current Cryptography Standards
• Simulation of Quantum Systems for Material Science
• Quantum Computing for Optimization Problems in Logistics and Manufacturing
• Theoretical Limits of Quantum Computing: Understanding Quantum Complexity
• Quantum Computing and the Future of Search Algorithms
• The Role of Quantum Computing in Climate Science and Environmental Modeling
• Quantum Annealing vs. Universal Quantum Computing: Comparative Studies
• Implementing Quantum Algorithms in Quantum Programming Languages
• The Impact of Quantum Computing on Public Key Cryptography
• Quantum Entanglement: Experiments and Applications in Quantum Networks
• Scalability Challenges in Quantum Processors
• The Ethics and Policy Implications of Quantum Computing
• Quantum Computing in Space Exploration and Astrophysics
• The Role of Quantum Computing in Developing Next-Generation AI Systems
• Quantum Computing in the Energy Sector: Applications in Smart Grids and Nuclear Fusion
• Noise and Decoherence in Quantum Computers: Overcoming Practical Challenges
• Quantum Computing for Predicting Economic Market Trends
• Quantum Sensors: Enhancing Precision in Measurement and Imaging
• The Future of Quantum Computing Education and Workforce Development
• Quantum Computing in Cybersecurity: Preparing for a Post-Quantum World
• Quantum Computing and the Internet of Things: Potential Intersections
• Practical Quantum Computing: From Theory to Real-World Applications
• Quantum Supremacy: Milestones and Future Goals
• The Role of Quantum Computing in Genetics and Genomics
• Quantum Computing for Material Discovery and Design
• The Challenges of Quantum Programming Languages and Environments
• Quantum Computing in Art and Creative Industries
• The Global Race for Quantum Computing Supremacy: Technological and Political Aspects
• Quantum Computing and Its Implications for Software Engineering
• Advances in Humanoid Robotics: New Developments and Challenges
• Robotics in Healthcare: From Surgery to Rehabilitation
• The Integration of AI in Robotics: Enhanced Autonomy and Learning Capabilities
• Swarm Robotics: Coordination Strategies and Applications
• The Use of Robotics in Hazardous Environments: Deep Sea and Space Exploration
• Soft Robotics: Materials, Design, and Applications
• Robotics in Agriculture: Automation of Farming and Harvesting Processes
• The Role of Robotics in Manufacturing: Increased Efficiency and Flexibility
• Ethical Considerations in the Deployment of Robots in Human Environments
• Autonomous Vehicles: Technological Advances and Regulatory Challenges
• Robotic Assistants for the Elderly and Disabled: Improving Quality of Life
• The Use of Robotics in Education: Teaching Science, Technology, Engineering, and Math (STEM)
• Robotics and Computer Vision: Enhancing Perception and Decision Making
• The Impact of Robotics on Employment and the Workforce
• The Development of Robotic Systems for Environmental Monitoring and Conservation
• Machine Learning Techniques for Robotic Perception and Navigation
• Advances in Robotic Surgery: Precision and Outcomes
• Human-Robot Interaction: Building Trust and Cooperation
• Robotics in Retail: Automated Warehousing and Customer Service
• Energy-Efficient Robots: Design and Utilization
• Robotics in Construction: Automation and Safety Improvements
• The Role of Robotics in Disaster Response and Recovery Operations
• The Application of Robotics in Art and Creative Industries
• Robotics and the Future of Personal Transportation
• Ethical AI in Robotics: Ensuring Safe and Fair Decision-Making
• The Use of Robotics in Logistics: Drones and Autonomous Delivery Vehicles
• Robotics in the Food Industry: From Production to Service
• The Integration of IoT with Robotics for Enhanced Connectivity
• Wearable Robotics: Exoskeletons for Rehabilitation and Enhanced Mobility
• The Impact of Robotics on Privacy and Security
• Robotic Pet Companions: Social Robots and Their Psychological Effects
• Robotics for Planetary Exploration and Colonization
• Underwater Robotics: Innovations in Oceanography and Marine Biology
• Advances in Robotics Programming Languages and Tools
• The Role of Robotics in Minimizing Human Exposure to Contaminants and Pathogens
• Collaborative Robots (Cobots): Working Alongside Humans in Shared Spaces
• The Use of Robotics in Entertainment and Sports
• Robotics and Machine Ethics: Programming Moral Decision-Making
• The Future of Military Robotics: Opportunities and Challenges
• Sustainable Robotics: Reducing the Environmental Impact of Robotic Systems
• Agile Methodologies: Evolution and Future Trends
• DevOps Practices: Improving Software Delivery and Lifecycle Management
• The Impact of Microservices Architecture on Software Development
• Containerization Technologies: Docker, Kubernetes, and Beyond
• Software Quality Assurance: Modern Techniques and Tools
• The Role of Artificial Intelligence in Automated Software Testing
• Blockchain Applications in Software Development and Security
• The Integration of Continuous Integration and Continuous Deployment (CI/CD) in Software Projects
• Cybersecurity in Software Engineering: Best Practices for Secure Coding
• Low-Code and No-Code Development: Implications for Professional Software Development
• The Future of Software Engineering Education
• Software Sustainability: Developing Green Software and Reducing Carbon Footprints
• The Role of Software Engineering in Healthcare: Telemedicine and Patient Data Management
• Privacy by Design: Incorporating Privacy Features at the Development Stage
• The Impact of Quantum Computing on Software Engineering
• Software Engineering for Augmented and Virtual Reality: Challenges and Innovations
• Cloud-Native Applications: Design, Development, and Deployment
• Software Project Management: Agile vs. Traditional Approaches
• Open Source Software: Community Engagement and Project Sustainability
• The Evolution of Graphical User Interfaces in Application Development
• The Challenges of Integrating IoT Devices into Software Systems
• Ethical Issues in Software Engineering: Bias, Accountability, and Regulation
• Software Engineering for Autonomous Vehicles: Safety and Regulatory Considerations
• Big Data Analytics in Software Development: Enhancing Decision-Making Processes
• The Future of Mobile App Development: Trends and Technologies
• The Role of Software Engineering in Artificial Intelligence: Frameworks and Algorithms
• Performance Optimization in Software Applications
• Adaptive Software Development: Responding to Changing User Needs
• Software Engineering in Financial Services: Compliance and Security Challenges
• User Experience (UX) Design in Software Engineering
• The Role of Software Engineering in Smart Cities: Infrastructure and Services
• The Impact of 5G on Software Development and Deployment
• Real-Time Systems in Software Engineering: Design and Implementation Challenges
• Cross-Platform Development Challenges: Ensuring Consistency and Performance
• Software Testing Automation: Tools and Trends
• The Integration of Cyber-Physical Systems in Software Engineering
• Software Engineering in the Entertainment Industry: Game Development and Beyond
• The Application of Machine Learning in Predicting Software Bugs
• The Role of Software Engineering in Cybersecurity Defense Strategies
• Accessibility in Software Engineering: Creating Inclusive and Usable Software
• Progressive Web Apps (PWAs): Advantages and Implementation Challenges
• The Future of Web Accessibility: Standards and Practices
• Single-Page Applications (SPAs) vs. Multi-Page Applications (MPAs): Performance and Usability
• The Impact of Serverless Computing on Web Development
• The Evolution of CSS for Modern Web Design
• Security Best Practices in Web Development: Defending Against XSS and CSRF Attacks
• The Role of Web Development in Enhancing E-commerce User Experience
• The Use of Artificial Intelligence in Web Personalization and User Engagement
• The Future of Web APIs: Standards, Security, and Scalability
• Responsive Web Design: Techniques and Trends
• JavaScript Frameworks: Vue.js, React.js, and Angular – A Comparative Analysis
• Web Development for IoT: Interfaces and Connectivity Solutions
• The Impact of 5G on Web Development and User Experiences
• The Use of Blockchain Technology in Web Development for Enhanced Security
• Web Development in the Cloud: Using AWS, Azure, and Google Cloud
• Content Management Systems (CMS): Trends and Future Developments
• The Application of Web Development in Virtual and Augmented Reality
• The Importance of Web Performance Optimization: Tools and Techniques
• Sustainable Web Design: Practices for Reducing Energy Consumption
• The Role of Web Development in Digital Marketing: SEO and Social Media Integration
• Headless CMS: Benefits and Challenges for Developers and Content Creators
• The Future of Web Typography: Design, Accessibility, and Performance
• Web Development and Data Protection: Complying with GDPR and Other Regulations
• Real-Time Web Communication: Technologies like WebSockets and WebRTC
• Front-End Development Tools: Efficiency and Innovation in Workflow
• The Challenges of Migrating Legacy Systems to Modern Web Architectures
• Microfrontends Architecture: Designing Scalable and Decoupled Web Applications
• The Impact of Cryptocurrencies on Web Payment Systems
• User-Centered Design in Web Development: Methods for Engaging Users
• The Role of Web Development in Business Intelligence: Dashboards and Reporting Tools
• Web Development for Mobile Platforms: Optimization and Best Practices
• The Evolution of E-commerce Platforms: From Web to Mobile Commerce
• Web Security in E-commerce: Protecting Transactions and User Data
• Dynamic Web Content: Server-Side vs. Client-Side Rendering
• The Future of Full Stack Development: Trends and Skills
• Web Design Psychology: How Design Influences User Behavior
• The Role of Web Development in the Non-Profit Sector: Fundraising and Community Engagement
• The Integration of AI Chatbots in Web Development
• The Use of Motion UI in Web Design: Enhancing Aesthetics and User Interaction
• The Future of Web Development: Predictions and Emerging Technologies

We trust that this comprehensive list of computer science thesis topics will serve as a valuable starting point for your research endeavors. With 1000 unique and carefully selected topics distributed across 25 key areas of computer science, students are equipped to tackle complex questions and contribute meaningful advancements to the field. As you proceed to select your thesis topic, consider not only your personal interests and career goals but also the potential impact of your research. We encourage you to explore these topics thoroughly and choose one that will not only challenge you but also push the boundaries of technology and innovation.

The Range of Computer Science Thesis Topics

Computer science stands as a dynamic and ever-evolving field that continuously reshapes how we interact with the world. At its core, the discipline encompasses not just the study of algorithms and computation, but a broad spectrum of practical and theoretical knowledge areas that drive innovation in various sectors. This article aims to explore the rich landscape of computer science thesis topics, offering students and researchers a glimpse into the potential areas of study that not only challenge the intellect but also contribute significantly to technological progress. As we delve into the current issues, recent trends, and future directions of computer science, it becomes evident that the possibilities for research are both vast and diverse. Whether you are intrigued by the complexities of artificial intelligence, the robust architecture of networks and systems, or the innovative approaches in cybersecurity, computer science offers a fertile ground for developing thesis topics that are as impactful as they are intellectually stimulating.

Current Issues in Computer Science

One of the prominent current issues in computer science revolves around data security and privacy. As digital transformation accelerates across industries, the massive influx of data generated poses significant challenges in terms of its protection and ethical use. Cybersecurity threats have become more sophisticated, with data breaches and cyber-attacks causing major concerns for organizations worldwide. This ongoing battle demands continuous improvements in security protocols and the development of robust cybersecurity measures. Computer science thesis topics in this area can explore new cryptographic methods, intrusion detection systems, and secure communication protocols to fortify digital defenses. Research could also delve into the ethical implications of data collection and use, proposing frameworks that ensure privacy while still leveraging data for innovation.

Another critical issue facing the field of computer science is the ethical development and deployment of artificial intelligence (AI) systems. As AI technologies become more integrated into daily life and critical infrastructure, concerns about bias, fairness, and accountability in AI systems have intensified. Thesis topics could focus on developing algorithms that address these ethical concerns, including techniques for reducing bias in machine learning models and methods for increasing transparency and explainability in AI decisions. This research is crucial for ensuring that AI technologies promote fairness and do not perpetuate or exacerbate existing societal inequalities.

Furthermore, the rapid pace of technological change presents a challenge in terms of sustainability and environmental impact. The energy consumption of large data centers, the carbon footprint of producing and disposing of electronic waste, and the broader effects of high-tech innovations on the environment are significant concerns within computer science. Thesis research in this domain could focus on creating more energy-efficient computing methods, developing algorithms that reduce power consumption, or innovating recycling technologies that address the issue of e-waste. This research not only contributes to the field of computer science but also plays a crucial role in ensuring that technological advancement does not come at an unsustainable cost to the environment.

These current issues highlight the dynamic nature of computer science and its direct impact on society. Addressing these challenges through focused research and innovative thesis topics not only advances the field but also contributes to resolving some of the most pressing problems facing our global community today.

Recent Trends in Computer Science

In recent years, computer science has witnessed significant advancements in the integration of artificial intelligence (AI) and machine learning (ML) across various sectors, marking one of the most exciting trends in the field. These technologies are not just reshaping traditional industries but are also at the forefront of driving innovations in areas like healthcare, finance, and autonomous systems. Thesis topics within this trend could explore the development of advanced ML algorithms that enhance predictive analytics, improve automated decision-making, or refine natural language processing capabilities. Additionally, AI’s role in ethical decision-making and its societal impacts offers a rich vein of inquiry for research, focusing on mitigating biases and ensuring that AI systems operate transparently and justly.

Another prominent trend in computer science is the rapid growth of blockchain technology beyond its initial application in cryptocurrencies. Blockchain is proving its potential in creating more secure, decentralized, and transparent networks for a variety of applications, from enhancing supply chain logistics to revolutionizing digital identity verification processes. Computer science thesis topics could investigate novel uses of blockchain for ensuring data integrity in digital transactions, enhancing cybersecurity measures, or even developing new frameworks for blockchain integration into existing technological infrastructures. The exploration of blockchain’s scalability, speed, and energy consumption also presents critical research opportunities that are timely and relevant.

Furthermore, the expansion of the Internet of Things (IoT) continues to be a significant trend, with more devices becoming connected every day, leading to increasingly smart environments. This proliferation poses unique challenges and opportunities for computer science research, particularly in terms of scalability, security, and new data management strategies. Thesis topics might focus on optimizing network protocols to handle the massive influx of data from IoT devices, developing solutions to safeguard against IoT-specific security vulnerabilities, or innovative applications of IoT in urban planning, smart homes, or healthcare. Research in this area is crucial for advancing the efficiency and functionality of IoT systems and for ensuring they can be safely and effectively integrated into modern life.

These recent trends underscore the vibrant and ever-evolving nature of computer science, reflecting its capacity to influence and transform an array of sectors through technological innovation. The continual emergence of new research topics within these trends not only enriches the academic discipline but also provides substantial benefits to society by addressing practical challenges and enhancing the capabilities of technology in everyday life.

Future Directions in Computer Science

As we look toward the future, one of the most anticipated areas in computer science is the advancement of quantum computing. This emerging technology promises to revolutionize problem-solving in fields that require immense computational power, such as cryptography, drug discovery, and complex system modeling. Quantum computing has the potential to process tasks at speeds unachievable by classical computers, offering breakthroughs in materials science and encryption methods. Computer science thesis topics might explore the theoretical underpinnings of quantum algorithms, the development of quantum-resistant cryptographic systems, or practical applications of quantum computing in industry-specific scenarios. Research in this area not only contributes to the foundational knowledge of quantum mechanics but also paves the way for its integration into mainstream computing, marking a significant leap forward in computational capabilities.

Another promising direction in computer science is the advancement of autonomous systems, particularly in robotics and vehicle automation. The future of autonomous technologies hinges on improving their safety, reliability, and decision-making processes under uncertain conditions. Thesis topics could focus on the enhancement of machine perception through computer vision and sensor fusion, the development of more sophisticated AI-driven decision frameworks, or ethical considerations in the deployment of autonomous systems. As these technologies become increasingly prevalent, research will play a crucial role in addressing the societal and technical challenges they present, ensuring their beneficial integration into daily life and industry operations.

Additionally, the ongoing expansion of artificial intelligence applications poses significant future directions for research, especially in the realm of AI ethics and policy. As AI systems become more capable and widespread, their impact on privacy, employment, and societal norms continues to grow. Future thesis topics might delve into the development of guidelines and frameworks for responsible AI, studies on the impact of AI on workforce dynamics, or innovations in transparent and fair AI systems. This research is vital for guiding the ethical evolution of AI technologies, ensuring they enhance societal well-being without diminishing human dignity or autonomy.

These future directions in computer science not only highlight the field’s potential for substantial technological advancements but also underscore the importance of thoughtful consideration of their broader implications. By exploring these areas in depth, computer science research can lead the way in not just technological innovation, but also in shaping a future where technology and ethics coexist harmoniously for the betterment of society.

In conclusion, the field of computer science is not only foundational to the technological advancements that characterize the modern age but also crucial in solving some of the most pressing challenges of our time. The potential thesis topics discussed in this article reflect a mere fraction of the opportunities that lie in the realms of theory, application, and innovation within this expansive field. As emerging technologies such as quantum computing, artificial intelligence, and blockchain continue to evolve, they open new avenues for research that could potentially redefine existing paradigms. For students embarking on their thesis journey, it is essential to choose a topic that not only aligns with their academic passions but also contributes to the ongoing expansion of computer science knowledge. By pushing the boundaries of what is known and exploring uncharted territories, students can leave a lasting impact on the field and pave the way for future technological breakthroughs. As we look forward, it’s clear that computer science will continue to be a key driver of change, making it an exciting and rewarding area for academic and professional growth.

Thesis Writing Services by iResearchNet

At iResearchNet, we specialize in providing exceptional thesis writing services tailored to meet the diverse needs of students, particularly those pursuing advanced topics in computer science. Understanding the pivotal role a thesis plays in a student’s academic career, we offer a suite of services designed to assist students in crafting papers that are not only well-researched and insightful but also perfectly aligned with their academic objectives. Here are the key features of our thesis writing services:

• Expert Degree-Holding Writers : Our team consists of writers who hold advanced degrees in computer science and related fields. Their academic and professional backgrounds ensure that they bring a wealth of knowledge and expertise to your thesis.
• Custom Written Works : Every thesis we produce is tailor-made to meet the specific requirements and guidelines provided by the student. This bespoke approach ensures that each paper is unique and of the highest quality.
• In-depth Research : We pride ourselves on conducting thorough and comprehensive research for every thesis. Our writers utilize the latest resources, databases, and scholarly articles to gather the most relevant and up-to-date information.
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Welcome to the on-line version of the UNC dissertation proposal collection. The purpose of this collection is to provide examples of proposals for those of you who are thinking of writing a proposal of your own. I hope that this on-line collection proves to be more difficult to misplace than the physical collection that periodically disappears. If you are preparing to write a proposal you should make a point of reading the excellent document The Path to the Ph.D., written by James Coggins. It includes advice about selecting a topic, preparing a proposal, taking your oral exam and finishing your dissertation. It also includes accounts by many people about the process that each of them went through to find a thesis topic. Adding to the Collection This collection of proposals becomes more useful with each new proposal that is added. If you have an accepted proposal, please help by including it in this collection. You may notice that the bulk of the proposals currently in this collection are in the area of computer graphics. This is an artifact of me knowing more computer graphics folks to pester for their proposals. Add your non-graphics proposal to the collection and help remedy this imbalance! There are only two requirements for a UNC proposal to be added to this collection. The first requirement is that your proposal must be completely approved by your committee. If we adhere to this, then each proposal in the collection serves as an example of a document that five faculty members have signed off on. The second requirement is that you supply, as best you can, exactly the document that your committee approved. While reading over my own proposal I winced at a few of the things that I had written. I resisted the temptation to change the document, however, because this collection should truely reflect what an accepted thesis proposal looks like. Note that there is no requirement that the author has finished his/her Ph.D. Several of the proposals in the collection were written by people who, as of this writing, are still working on their dissertation. This is fine! I encourage people to submit their proposals in any form they wish. Perhaps the most useful forms at the present are Postscript and HTML, but this may not always be so. Greg Coombe has generously provided LaTeX thesis style files , which, he says, conform to the 2004-2005 stlye requirements.

Many thanks to everyone who contributed to this collection!

Greg Coombe, "Incremental Construction of Surface Light Fields" in PDF . Karl Hillesland, "Image-Based Modelling Using Nonlinear Function Fitting on a Stream Architecture" in PDF . Martin Isenburg, "Compressing, Streaming, and Processing of Large Polygon Meshes" in PDF . Ajith Mascarenhas, "A Topological Framework for Visualizing Time-varying Volumetric Datasets" in PDF . Josh Steinhurst, "Practical Photon Mapping in Hardware" in PDF . Ronald Azuma, "Predictive Tracking for Head-Mounted Displays," in Postscript Mike Bajura, "Virtual Reality Meets Computer Vision," in Postscript David Ellsworth, "Polygon Rendering for Interactive Scientific Visualization on Multicomputers," in Postscript Richard Holloway, "A Systems-Engineering Study of the Registration Errors in a Virtual-Environment System for Cranio-Facial Surgery Planning," in Postscript Victoria Interrante, "Uses of Shading Techniques, Artistic Devices and Interaction to Improve the Visual Understanding of Multiple Interpenetrating Volume Data Sets," in Postscript Mark Mine, "Modeling From Within: A Proposal for the Investigation of Modeling Within the Immersive Environment" in Postscript Steve Molnar, "High-Speed Rendering using Scan-Line Image Composition," in Postscript Carl Mueller, " High-Performance Rendering via the Sort-First Architecture ," in Postscript Ulrich Neumann, "Direct Volume Rendering on Multicomputers," in Postscript Marc Olano, "Programmability in an Interactive Graphics Pipeline," in Postscript Krish Ponamgi, "Collision Detection for Interactive Environments and Simulations," in Postscript Russell Taylor, "Nanomanipulator Proposal," in Postscript Greg Turk, " Generating Textures on Arbitrary Surfaces ," in HTML and Postscript Terry Yoo, " Statistical Control of Nonlinear Diffusion ," in Postscript

How to Draft Statement of Purpose (SOP) Computer Science PhD? (Sample Included)

• Post author: admin
• Post published: November 29, 2023
• Post category: SOP
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Imagine applying for a Computer Science PhD is like setting out on a thrilling adventure. Now, at the heart of this adventure is a document that holds the key to your academic dreams—the Statement of Purpose (SOP). It might sound like a fancy term, but think of it as your personal story, told in a formal way, showcasing your love for learning and your big dreams in research.

The SOP isn’t just a box to tick; it’s more like your self-painted portrait. This document, carefully crafted, lets you share your academic journey and spill the beans on why you’re excited about diving deep into Computer Science. In the world of PhD applications, especially in Computer Science, the SOP is your secret weapon.

It not only shows off your smarts in academics but also reveals your passion for exploring new frontiers in research. So, let’s break it down and see how you can turn this piece of paperwork into a compelling story that makes you stand out!

Structure of a Strong SOP for Computer Science PhD

Alright, let’s break down the SOP into bite-sized pieces to create a roadmap that admissions committees can effortlessly follow.

Introduction: A Captivating Kickoff

• Start your SOP with a bang! Craft an introduction that grabs attention.
• Keep it concise but powerful, setting the stage for what’s to come.
• Use this section to hint at your passion for Computer Science and why you’re ready to dive deep.

Academic Background: Your Educational Canvas

• Paint a picture of your academic journey so far.
• Highlight key courses, projects, or achievements that shaped your love for Computer Science.
• Don’t just list, narrate. Share the story of your academic evolution.

Research Experience: Unveiling Your Investigative Side

• Showcase any research projects or experiences you’ve had.
• Emphasize not just what you did but what you learned from each experience.
• Connect your research ventures to your passion for advancing knowledge in Computer Science.

Future Goals: Casting Your Academic Vision

• Envision the future! What do you aspire to achieve with a Computer Science PhD?
• Be specific about how this particular program aligns with your goals.
• Convey a sense of excitement about the impact you aim to make in the field.

Tips for a Cohesive Flow:

• Thread of Continuity: Ensure a smooth transition between sections. Let one idea naturally flow into the next.
• Connect the Dots: Clearly show how each section contributes to the bigger picture—your journey and your aspirations.
• Avoid Repetition: Be mindful not to repeat information. Each section should add a new layer to your story.
• Maintain Clarity: Use straightforward language. Remember, you’re telling a story, not penning a mystery novel.
• Pacing is Key: Don’t rush. Give each section the attention it deserves, balancing details without overwhelming the reader.
• Reflect Your Voice: Let your personality shine through. An SOP is not just about facts; it’s about you.

By following this roadmap, your SOP becomes a compelling narrative that not only checks the boxes but leaves a lasting impression on those reviewing your application. Now, let’s dive into each section and discover how to make your SOP a standout piece in the world of Computer Science PhD applications!

How to Tailor Your SOP for a Computer Science PhD: Crafting a Stellar Narrative

Tailoring your Statement of Purpose (SOP) for a Computer Science PhD is akin to creating a bespoke masterpiece. Here’s your guide to weaving a narrative that not only stands out but also resonates with the unique vibe of the Computer Science academic realm.

Precision in Passion: Illuminate Your Unique Spark

• Engage with Details: Dive into the specific aspects of Computer Science that light the fire in your academic soul.
• Steer Clear of Generalities: Avoid vague statements; instead, pinpoint the precise areas that fuel your passion.
• Why Here, Why Now: Clearly articulate why pursuing a PhD in Computer Science is the next logical step for you, especially at this particular institution.

Aligning Stars: Mapping Your Journey to the Program

• In-Depth Program Research: Showcase your familiarity with the program’s strengths, faculty, and distinctive features.
• Demonstrate Fit: Explicitly align your research interests with what the program specializes in.
• Highlight Synergy: Illustrate how your academic journey seamlessly integrates with the unique offerings of the program.

Unique Contributions: Spotlight Your Distinctive Brilliance

• Unveil Your Uniqueness: Showcase skills, experiences, or perspectives that make you stand out.
• Contribution Quotient: Emphasize how your presence will enrich the academic community.
• Connect the Dots: Demonstrate how your background aligns with the ethos and culture of the program.

Previous Collaborations: Weaving a Tapestry of Connection

• Faculty Interactions: If you’ve interacted with faculty members before, mention these experiences.
• Seamless Continuity: Illustrate how these interactions have influenced your decision to pursue a PhD in Computer Science.
• Building Bridges: Show that you’re not just an applicant but someone who already shares a connection with the academic community.

Research Synergy: Harmonizing Your Goals with Program Initiatives

• Concrete Examples: Discuss specific research initiatives within the program that resonate with your interests.
• Showcase Alignment: Use tangible examples to illustrate how your research goals complement the ongoing work within the department.
• Paint a Collaborative Vision: Convey how your research contributions can seamlessly integrate with the existing research landscape.

Forward-Looking Fit: Crafting a Visionary Finale

• Future Research Aspirations: Share your vision for future research endeavors and how the program acts as the catalyst.
• Resource Utilization: Illustrate how the program’s resources, faculty mentorship, and collaborative environment will propel your academic ambitions.
• Infuse Excitement: Convey a sense of eagerness for the journey ahead, painting a vivid picture of the exciting possibilities within your grasp.

Showcasing Academic Background for a Computer Science PhD: Crafting Your Academic Narrative

Your academic background is the canvas upon which you paint the story of your readiness for a Computer Science PhD. Make this narrative captivating by strategically presenting your achievements. Start by delving into specific courses, projects, or research experiences that highlight your prowess in the realm of Computer Science.

Instead of a mere laundry list, narrate the significance of each academic milestone, showcasing how it has fueled your passion and prepared you for the challenges and innovations integral to a PhD journey.

Emphasizing Research Experience for a Computer Science PhD: Unveiling Your Investigative Journey

In the intricate tapestry of your Statement of Purpose (SOP) for a Computer Science PhD, the spotlight on your research experience is akin to revealing the heart of your academic journey. Elevate the significance of detailing your research escapades; this is your chance to showcase your prowess in tackling real-world challenges and contributing to the evolving landscape of Computer Science.

When delving into your research experience, don’t merely list projects—narrate them. Provide a window into your contributions, methodologies, and outcomes. Break down the complexity of your work, ensuring that the reader not only comprehends your technical prowess but also appreciates the tangible impact of your research.

Aligning with Faculty and Research Opportunities: Forging Connections in Your Computer Science PhD Journey

Navigating the labyrinth of a Computer Science PhD application involves not only aligning with the program but also forging connections with the academic trailblazers—faculty members. Understanding the pivotal role that faculty play in shaping your academic odyssey, it’s crucial to delve into the significance of researching their work. You can use resources like LinkedIn to connect with faculty members.

Take the time to explore the research portfolios of faculty members within the Computer Science department. Uncover their contributions to the field, ongoing projects, and areas of expertise. Expressing genuine alignment with specific faculty members in your Statement of Purpose (SOP) isn’t just a formality; it’s a strategic move that showcases your investment in the program and your vision for collaborative research.

Addressing Potential Weaknesses: Navigating Challenges with Transparency and Resilience

In the candid narrative of your Statement of Purpose (SOP) for a Computer Science PhD, addressing potential weaknesses becomes an art of transparency and resilience. Rather than sidestepping challenges, use this opportunity to showcase your ability to navigate them with honesty and determination.

  If there are gaps or weaknesses in your academic or research background, embrace them with transparency. Acknowledge the hurdles you’ve faced and elucidate the steps taken to overcome them. Whether it’s a dip in grades during a particular semester or a shift in research focus, be forthright about the circumstances. However, don’t stop there—highlight the lessons learned, the skills gained, and the resilience fostered through these experiences.

Editing and Proofreading Tips: Polishing Your Computer Science PhD SOP to Perfection

In the final lap of crafting your Statement of Purpose (SOP) for a Computer Science PhD, the spotlight shifts to the crucial phase of editing and proofreading. This meticulous process is not just about fixing typos; it’s about sculpting a narrative that sparkles with clarity, conciseness, and error-free precision.

• Clarity is Key:
• Readability Check: Ensure your SOP is easily digestible. Break down complex sentences and avoid jargon.
• Logical Flow: Confirm that your ideas progress logically. Each paragraph should seamlessly lead to the next.
• Conciseness Matters:
• Trim the Fat: Weed out unnecessary details. Every word should contribute to your narrative.
• Brevity with Impact: Be concise, but make each sentence count. Quality over quantity is the mantra.
• Error-Free Zone:
• Grammar Guru: Scrutinize grammar and punctuation. Consider tools like Grammarly for a thorough check.
• Precision Matters: Accuracy in conveying your ideas is non-negotiable. Review facts, figures, and technical terms for precision.
• External Perspectives:
• Fresh Eyes: Ask a friend or mentor to review your SOP. A fresh perspective can catch overlooked errors.
• Alignment with Guidelines: Ensure your SOP aligns with the program’s guidelines. Adhering to specified word limits and formatting is crucial.
• SEO-friendly Touch:
• Strategic Keywords: Integrate relevant keywords organically, such as “Computer Science PhD,” “academic journey,” and “research aspirations.”
• Meta Tags: Optimize meta tags and descriptions with program-specific terms for increased online visibility.
• Read-Aloud Ritual:
• Auditory Check: Read your SOP aloud. This helps catch awkward phrasing and ensures a smooth, engaging rhythm.

Sample Computer Science Statement of Purpose (SOP)

To help you have a good head start, feel free to refer our sample SOP which is tailored specifically for PhD in Computer Science –

Sample Statement of Purpose for Computer Science PhD

FAQ Section: Your Queries, Answered

Q1: what makes a strong statement of purpose (sop) for a computer science phd.

A: A strong SOP for a Computer Science PhD is one that vividly communicates your passion, aligns with the program’s offerings, and showcases your academic and research journey. Be specific about your academic background, research experiences, and future goals. Tailor your SOP to resonate with the program and faculty, highlighting unique contributions you can bring to the academic community.

Q2: How should I address potential weaknesses in my academic or research background?

A: Addressing weaknesses in your SOP is an opportunity to display transparency and resilience. Acknowledge any gaps or challenges, and then emphasize the steps you’ve taken to overcome them. Highlight the lessons learned and skills gained from these experiences, demonstrating your ability to turn obstacles into opportunities for growth.

Q3: How can I align my SOP with specific faculty members and their research in the Computer Science PhD program?

A: Research faculty members thoroughly by exploring their work, ongoing projects, and areas of expertise. Express genuine alignment with specific faculty members in your SOP, citing their work that resonates with your research interests. Be authentic in showcasing how their expertise complements your academic aspirations, indicating a readiness to contribute meaningfully to their research initiatives.

Q4: What are essential proofreading tips to ensure a polished SOP?

A: To ensure a polished SOP, focus on clarity, conciseness, and error-free writing. Check for readability and logical flow, trim unnecessary details, and meticulously proofread for grammar and punctuation. Seek external perspectives for fresh insights, adhere to program guidelines, and incorporate relevant SEO-friendly keywords to optimize your SOP for search engines.

Q5: How do I make my SOP stand out in the competitive landscape of Computer Science PhD applications?

A: To make your SOP stand out, craft a compelling narrative by emphasizing your passion, unique contributions, and alignment with the program and faculty. Showcase specific examples of your academic and research achievements, articulate future goals, and demonstrate a clear understanding of how the program will support your aspirations. Engage the reader with authenticity and a well-structured, error-free narrative.

Closing Thoughts: Embarking on Your Computer Science PhD Journey

As you conclude the compelling narrative of your Statement of Purpose (SOP) for a Computer Science PhD, remember that this document is not just a reflection of your academic journey but a testament to your aspirations and resilience.

The road to a PhD is paved with challenges, but it is also a journey of self-discovery and scholarly growth. Take a moment to reflect on the milestones you’ve achieved and the intellectual terrain you’re eager to explore.

Your SOP is not merely a formality; it is your voice in the competitive landscape of PhD applications, resonating with the vibrancy and innovation that characterize the field of Computer Science. Also, feel free to go through our guide on the best universities for Computer Science in UK.

As you embark on this transformative journey, keep in mind that each word in your SOP holds the power to shape your academic future. Be genuine, be bold, and let your passion shine through every sentence. The challenges ahead are not obstacles but opportunities for intellectual triumphs and groundbreaking contributions.

Should you have any lingering questions or wish to share your experiences, I invite you to engage in the comments below. Your insights and queries are not only valuable to you but also to the broader community navigating the exciting terrain of Computer Science PhD applications.

Remember, the journey you are embarking upon is both profound and rewarding. Best of luck as you set forth on this academic odyssey, and may your SOP pave the way for an enriching and fulfilling pursuit of a Computer Science PhD.

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Discussion on Ph.D. thesis proposals in computing science

1. introduction, 2. what is a thesis proposal, 3. problem statement and background, 4. the candidate's ideas, 5. the shape of the solutions, 6. plan of action and outline of the thesis, 8. note and acknowledgement.

Finding problem statement for PhD Research – A methodical step-wise guide

A problem statement is just as it sounds; revealing the problem in the form of a statement. Your problem statement is the issue you wish to resolve and fill the gap in the literature of your field. It is the building block of your research, solely responsible to hold the whole process. You should cover your statement in a maximum of 300 words in an area of your interest. The area in which you are supposed to work is usually known beforehand and that is how you find your problem statement. The process to find a problem statement is as follows :

• The first step is the thinking process. You have to think of a number of ideas out of which one can be turned into a topic for the research. You should not focus on what you should write in your paper rather the focus should be on what you should know in your field. The question of what you should know will build up your interest in the area and you will not lose throughout the research course. While thinking of the topic, you have to be open-minded as what may come with the idea. The process includes a broader perspective to ponder upon.
• The next step is to make a list of all the ideas that pop up in your head to narrow them down and see how far the idea can take you in your research. Read the recent researches and journals or browse through the internet to filter your ideas. You must examine all the jotted ideas to work on and refine them. Choose the best-suited topic for your research out of your filtered ideas.
• Now, you should identify your chosen concept or the topic that will make up the problem statement. You should simplify the variables of your topic to develop it. You should focus on identifying nouns and phrases out of the topic.
• After you are done with phrasing the variables out of your topic and research issue, you should start studying the literature of the topic. Reviewing the literature on the chosen topic will broaden your idea to refine and reframe your research problem. As a researcher, you need to have a profound knowledge on the topic you are working on. This step may take a long time as you study and review the history of your topic.
• After you are clear about the history of the topic you should start with searching for the sources to broaden, modify or strengthen your argument. The data should be a source of criticism, new ideas and historical context. You should be able to broaden your concept with the collected data and lighten up the topic. The search for the sources serves as exploring the topic as well. This takes you in-depth of your topic.
• The final step is to outline your paper. Considering the hypothetical resolution in your mind, outline your paper and see if it leads you towards the end. If it does takes you to the desired results you should propose your research question and if it doesn’t then you need to further research for your problem statement.

The process of finding the problem statement is itself a tiring job and it comes with a set of conditions with it.

• The hunt for the problem should begin early and you should take the help of your advisor/supervisor while selecting the problem statement.
• Your problem statement should have a resolution, it should have a planned method to be resolved and bridge the gap in the history.
• Your resolution of the issue should bring a change in the literature of your field.
• Your problem statement should lead you to further research. It should bring more questions for either you to resolve or for another researcher to research on. If it doesn’t lead you more queries then it would be a waste of time since the resolution of the problem would not bring a huge change and impact on the academic society.
• The selected problem statement should be worth spending time on as it lays the foundation of the research. Also, the statement decides the maturity of the candidate towards his study on the subject.

Therefore, to build your whole research one must choose the best topic no matter how much time it takes.

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Preparing a phd research proposal for computer science.

   A research proposal plays a critical role in PhD application and should be a unique and original knowledge contribution. Research proposals are utilized to induce potential supervisors and funders that the research work is worthy of their facilitation. This brief guide helps to write an excellent research proposal. It meant to think about the PhD research proposal in a more explicit, organized, and purposeful way. It also emphasizes the practical steps which lead to conducting the research work. A proper PhD proposal provides the scope and significance of the topic and procedure of the research work. A strong research proposal depends upon many aspects, including the essence of the research, quality of the concept, duration of the research work, and supervision from experts. Under the consideration of all aspects, some key guidelines are highlighted for better research study below:

Significance of the research proposal

• The research proposal should demonstrate the significance and the quality of the research
• The proposal explains the potential of the proposed research work and its future impact among the research community.
• The proposal highlights the novelty, uniqueness, and freshness of the research work
• Proposal elucidates the originality of the problem and illustrates the critical thinking and skills applied to prove the research problem.

Selection of the research topic

• The topic selection depends on many factors, such as
• Background and expertise of the student in the research topic
• The expertise of the supervisor
• Future impact of the research problem
• Researchability of the research topic
• Availability and feasibility of the tools and technologies to solve the research problem
• Feasibility of publications in top journals
• How does it impact the advancement of knowledge?

Scope of the Research

• Significance of the field of the research
• Identify the potential applications
• The impact of the research on the Industry/Academia/Society

Literature Survey

• Collect relevant research papers from the leading journals for the last 5-10 years in the area of research
• Carry out a comprehensive literature survey on the research topic
• Narrow down the research idea and finalize the title

Research Gap Analysis

• Find out the problem based on the survey, which is not addressed appropriately in the topic of the proposal.
• Identify the limitations in the existing research
• Why the problem is essential and how it is going to impact future research
• Find the potential opportunities for further research to fill the gaps in the research topic

Problem Statement

• The problem statement should be more concise and concrete description of a research problem based on the research gap
• Explores the relevance and significance of the research idea
• Clearly describe the existence of the problem and how to tackle it
• The problem statement should be researchable to tackle the research issue, feasible for development, and clearly address the relevant research problem effectively.

Aim and Objectives

• Precisely define the achievable outcome and the purpose of the research

The proposed methodology

• Defines the systematic plan of the proposed research work
• Define the methods, tools, and techniques employed to solve the research problem
• Describe the method of analysis
• Performance evaluation of the proposed research work

Experimental Software Requirements

• Software tools required to solve the research problem
• Operating systems, Programming Language, Programming Packages, Database, Research Tools, Graph Generator, Document Writer and Plagiarism Checking Tools

Potential Contributions of the Research

• The potential outcome of the research
• Achievements of the research work
• How the research contributions impact the Industry/Academia/Society

Conclusions

• Precise conclusion of the research proposal
• Latest references related to the research proposal cited appropriately with proper citation format such as APA (American Psychological Association), MLA (Modern Language Association), and so on.

Research Topics for Writing a PhD Proposal in Computer Science

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