All Questions

23
votes
3answers
1k views

What is known about solutions to sparse integer linear programming problems?

If I have a set of linear constraints in which each constraint has at most (say) 4 variables (all nonnegative and with {0,1} coefficients except for one variable that can have a -1 coefficient), what ...
5
votes
0answers
250 views

When designing an explicitly parallel language, what built in functions should be parallelized? [closed]

As stated by the title. Some examples that I would include would be map and conditionals. What other functions should be built in already parallel for users to expand on it?
46
votes
4answers
3k views

What are the best current lower bounds on 3SAT?

What are the best current lower bounds for time and circuit depth for 3SAT?
80
votes
10answers
13k views

What would it mean to disprove Church-Turing thesis?

Sorry for the catchy title. I want to understand, what should one have to do to disprove the Church-Turing thesis? Somewhere I read it's mathematically impossible to do it! Why? Turing, Rosser etc ...
22
votes
2answers
554 views

What evidence do we have for (and against) Unique Games Conjecture?

Subhash Khot's Unique Games Conjecture is one of active research areas in complexity theory. What evidence do we have for it? What evidence do we have against it?
55
votes
14answers
2k views

Where and how did computers help prove a theorem?

The purposes of this question is to collect examples from theoretical computer science where the systematic use of computers was helpful in building a conjecture that lead to a theorem, falsifying a ...
21
votes
4answers
442 views

Which results in complexity theory make essential use of uniformity?

A complexity class separation proof uses uniformity of complexity classes essentially if the proof does not prove the result for nonuniform version, for example proofs based on diagonalization (like ...
125
votes
28answers
18k views

Problems Between P and NPC

Factoring and graph isomorphism are problems in NP that are not known to be in P nor to be NP-Complete. What are some other (sufficiently different) natural problems that share this property? ...
16
votes
3answers
2k views

Can a nondeterministic finite automata (NDFA) be efficiently converted to a deterministic finite automata (DFA) in subexponential space/time?

Twenty years ago, I built an regular expression package that included conversions from regular expressions to a finite state machine (DFA) and supported a host of closed regular expression operations ...
13
votes
1answer
589 views

What are the historical roots of Milner's bigraphs?

Robin Milner defined bigraphs as a type of graphical structure with graph-like structure but where the nodes can be nested. They generalise process calculi like CCS and the $\pi$-calculus, but Milner ...
14
votes
2answers
871 views

How large a treewidth can a tree plus half the edges have?

Let G be a tree on 2n vertices. The treewidth of G, tw(G) = 1. Now suppose we add n edges to G to get a graph H. An easy upper bound on tw(H) is n + 1. Is this essentially the best possible? It ...
17
votes
2answers
611 views

H-free cut problem

Suppose you are given a connected, simple, undirected graph H. The H-free cut problem is defined as follows: Given a simple, undirected graph G, is there a cut (partition of vertices into two ...
25
votes
4answers
1k views

What specific evidence is there for P = RP?

RP is the class of problems decidable by a nondeterministic Turing machine that terminates in polynomial time, but that is also allowed one-sided error. P is the usual class of problems decidable by ...
-1
votes
2answers
562 views

Minimum spanning tree algorithm. [closed]

Is the following a valid algorithm for finding a minimum spanning tree? Given a weighted graph with unique weights, remove the all edges that are the highest cost edge in any cycle of the original ...
12
votes
2answers
605 views

Simple balanced trees with O(1) concat?

In Purely Functional Worst Case Constant Time Catenable Sorted Lists, Brodal et al. present purely functional balanced trees with O(1) concatenate and O(lg n) insert, delete, and find. The data ...
30
votes
2answers
2k views

Hierarchies in NP (under the assumption that P != NP)

Assuming that P != NP, I believe it has been shown that there are problems which are not in P and not NP-Complete. Graph Isomorphism is conjectured to be such a problem. Is there any evidence of more ...
23
votes
1answer
2k views

Consequences of Complete problems for NP intersects coNP

What are the consequences of having complete problems in $NP\cap coNP$?
64
votes
11answers
4k views

What are good references to understanding the proof of the PCP theorem?

I'm familiar with a lot of results that use the PCP theorem (mainly in approximating algorithms), but I've never come across a clear explanation of the PCP theorem (ie, that $\mathsf{NP} = \mathsf{PCP}...
20
votes
2answers
904 views

Succinct circuit representation of graphs

The complexity class PPAD (e.g. computing various Nash equilibria) can be defined as the set of total search problems polytime reducible to END OF THE LINE: END OF THE LINE: Given circuits S and P ...
23
votes
3answers
932 views

Graph Isomorphism and hidden subgroups

I'm trying to understand the relationship between graph isomorphism and the hidden subgroup problem. Is there a good reference for this ?
21
votes
1answer
289 views

A comparison of extractors in terms of tradeoffs between time, randomness and space ?

Is there a good survey that compares different extractors, concentrators and superconcentrators and lays out the best methods in terms of the tradeoff between randomness, time and space ?
114
votes
11answers
10k views

How hard is unshuffling a string?

A shuffle of two strings is formed by interspersing the characters into a new string, keeping the characters of each string in order. For example, MISSISSIPPI is a ...
8
votes
1answer
387 views

Best resources for string searching or pattern matching exercises

I would like to be somewhat good at string searching and pattern matching, could you point me to some good online resources? Exercise problems would be great. Thanks.
17
votes
3answers
732 views

Are there any known implementations for quantum computing constructs?

Quantum Computation is an active area of research that aims to take advantage of quantum physics (e.g. quantum entanglement) to advance the efficiency capabilities of computers (does not alter the ...
15
votes
1answer
749 views

Online transitive closure better than O(N^2) per edge addition

I'm looking for an online algorithm to maintain the transitive closure of a directed acyclic graph with a time complexity less than O(N^2) per edge addition. My current algorithm is like this: ...
15
votes
6answers
3k views

Complexity of the Fisher-Yates Shuffle Algorithm

This question is in regard to the Fisher-Yates algorithm for returning a random shuffle of a given array. The Wikipedia page says that its complexity is O(n), but I think that it is O(n log n). In ...
16
votes
1answer
538 views

Why is it important that the secret is at the end when signing with MD5?

it is often said that when using the MD5 algorithm to sign some arbitrary information, the shared secret has to be at the end. Why?
18
votes
0answers
456 views

To what extent MSO = WS1S, when adding relations?

[This question has been asked on MathOverflow with no luck a month ago.] Let me first clarify my definitions. For a word $w \in \Sigma^*$, with $\Sigma =\{a_1, \ldots, a_n\}$, I define two ...
24
votes
5answers
1k views

What are some career options for someone with a computer scientist master degree?

Other than going fully academic and getting a doctorate/post-doc, or going for a more or less 'standard' job in software development, what are some other career options in the full or semi theoretical ...
32
votes
4answers
842 views

Correspondence between complexity classes and logic

I took a class once on Computability and Logic. The material included a correlation between complexity / computability classes (R, RE, co-RE, P, NP, Logspace, ...) and Logics (Predicate calculus, ...
48
votes
12answers
3k views

What is the theoretical basis of imperative programming?

Functional programming has a theoretical basis in lambda calculus and combinatory logic. As someone involved with statistical computing, I find these concepts to be very useful for modeling. Is ...
8
votes
3answers
3k views

Is Deolalikar's 2010 proof that $P \ne NP$ correct?

There was recently a claimed proof that $P \ne NP$. Not long after its publication there were raised some issues with this proof. So ... is the proof correct or not ? (Please only answer this if you ...
20
votes
3answers
462 views

space-bounded TMs and oracles

In general, the query-tape for an oracle counts towards the space-complexity of a TM. However, it seems plausible to allow a write-only oracle-tape (such as is used in L-space reductions). Is such a ...
8
votes
1answer
182 views

Process modeling with fine-grained notions of location

Is anyone aware of any process algebraic (or related) formalisms that capture fine-grained location information? I'm familiar with ambients and bigraphs, which obviously have a location model, but ...
10
votes
1answer
288 views

Generalizing the FFT

Can the divide and conquer nature of the FFT be generalized to other transforms (z Transform, chirp, etc) automatically? Is there an algorithm that takes in a description of transform (I don't know ...
14
votes
2answers
967 views

What is the following variation on Set Cover known as?

What is the following variation on set cover known as? Given a set S, a collection C of subsets of S and a positive integer K, do there exist K sets in C such that every pair of elements of S lies in ...
8
votes
1answer
1k views

What are some effective heuristics to find the number of Hamiltonian paths in a rectangular grid?

A particular programming problem I came across recently reduces to finding hamiltonian paths in a rectangular grid that would look something like, ...
13
votes
2answers
823 views

What is a good special-case sorting algorithm?

I have a dataset which is a number of objects arranged in a 2-D grid. I know I have a strict ordering, increasing as you go left-to-right within each row, and increasing as top-to-bottom within each ...

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