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Questions tagged [complexity]

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8
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0answers
180 views

SAT Solvers and their applications

I've been reading and learning about SAT solvers this week. If they can solve problems with thousands of variable quickly haven't we practically solved ANY problem that can be reduced to it, including ...
3
votes
1answer
376 views

Is there a counterexample to this work?

Is there a counterexample to this claim https://arxiv.org/abs/1610.00353? They claim a $O(n^6)$ LP model with simulations to support. I think asking validity is not a reasonable problem. However ...
11
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0answers
267 views

Error in paper “Some NP-complete geometric problems”?

The paper in question: M.R. Garey, R.L. Graham and D.S. Johnson. Some NP-complete geometric problems . This paper proofs the NP-completeness of some well-known problems, such as the Steiner Tree ...
6
votes
1answer
195 views

Paths of length $p$ in a Graph, $p$ a prime

I came across the following decision problem, for which I wondered whether anybody of you came across a similar problem and can give me some insight on its nature/complexity. Given as input a ...
3
votes
0answers
169 views

Implications of resolving $BPP$ vs $PSPACE$

The relationship between the complexity classes $BPP$, $P$, and $NEXP$ is currently undetermined. We know that $P \neq EXP$ by the time hierarchy theorem, but we don't know if $BPP = P$ (as many ...
-1
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2answers
432 views

Are these problems in NP class?

${\bf New\ version}$ [Version 1.2] Let $f: \mathbb{N} \to \{0,1\}$ be a computable function, ${\bf Fin}(\mathbb{Z})$ be the set of all finite subsets of $\mathbb{Z}$, and $W: {\bf Fin}(\mathbb{Z}) \...
0
votes
1answer
112 views

Does $\textbf{PCP}[poly(n), O(1)] = \textbf{coRP}$?

Something has been buzzing me recently. It is well-known that $\textbf{PCP}[poly(n), 0] = \textbf{coRP}$, but does $\textbf{PCP}[poly(n), O(1)] = \textbf{coRP}$ ? I have found a proof for this ...
2
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1answer
82 views

Petri net termination

Termination is the following problem. Input: a Petri Net with initial marking Output: "yes" iff there exists an infinite firing sequence. The naive algorithm in the case of bounded nets for example ...
18
votes
1answer
478 views

Formally Verified Complexity Theory

Is there any ongoing project to formally verify the theorems and proofs of complexity theory using a proof assistant like Coq? Are there any boundaries to doing this?
1
vote
1answer
143 views

Complexity of the Schönhage–Strassen algorithm

In the Wikipedia article, the complexity is listed as $O(n \cdot \log (n) \cdot \log (\log (n)))$, where $n$ is the number of bits. Would the real bound be given by setting $n=\frac{b}{w}$, where $b$...
13
votes
1answer
296 views

Parallel Pebble Game on a Line

In the pebble game on a line there are N+1 nodes labelled 0 through N. The game starts with a pebble on node 0. If there is a pebble on node i, you can add or remove a pebble from node i+1. The goal ...
1
vote
0answers
97 views

How to shrink a very large sparse matrix [closed]

Let $A$ be a matrix where $A \in \mathbb{F}^{n^s \times n^s}$ and $s>2$. Assume $A$ is a sparse matrix where its rank $\leq n$ and that there is only constant number of non-zero elements in each ...
7
votes
2answers
239 views

Complexity of comparison unary>binary

What is the smallest widely-known complexity class to which $$\left\{\langle i,j\rangle\middle|\begin{array}{@{}l@{\ }l@{}} & i\ \text{is a unary encoding of a positive integer}\ \hat\imath\\\...
1
vote
1answer
83 views

Why does not the definition of NP problems care about the complexity of guessing? [closed]

I have a question regarding the definition of NP problems. According to that, a problem is in NP if one can guess a certificate of polynomial size in polynomial time. However, this definition does not ...
7
votes
1answer
132 views

What's the complexity of factoring over a set of generators (say in $GL_2$)?

In particular, if I have some char-0 field $k$ (let's take $\mathbb C$ for now) and I consider $G = GL_2(k)$ with arbitrary nontrivial distinct $A, B \in G$. Then for some $C \in GL_2(k)$ do we know ...
3
votes
0answers
72 views

Is there any work that relates the liveness of a Petri Net to the complexity of determining coverability?

I'm working on a problem where the formalism appears to be an abstraction of a kind of Petri net, and it is possible to construct an equivalent Petri net from this formalism with the same behavior. ...
12
votes
2answers
1k views

What exactly are the classes FP, FNP and TFNP?

In his book Computational Complexity, Papadimitriou defines FNP as follows: Suppose that $L$ is a language in NP. By Proposition 9.1, there is a polynomial-time decidable, polynomially balanced ...
15
votes
2answers
675 views

Are There Highly Symmetric NP- or P-complete Languages?

Does there exist $L$, an NP- or P-complete language which has some family of symmetry groups $G_n$ (or groupoid, but then the algorithmic questions become more open) acting (in polynomial time) on ...
10
votes
2answers
138 views

Complexity of Computing Lexicographically Minimal Element of Orbit

Given strong generators for a group $(G \leq S_n, *)$ acting on bitstrings of length $n$ and an element $s \in \{0, 1\}^n$, how hard is it to compute the lexicographically minimal element of $G.s$, ...
2
votes
2answers
272 views

Formally proving no algorithm exists [closed]

Are there standard techniques to show that no algorithms exist for given complexity constraints? For example, consider the following problem. The input is a list of items with exactly one duplicate, ...
1
vote
0answers
151 views

Why does this algorithm not have an exponential complexity? [closed]

In this article : Kinodynamic Motion Planning B. Donald, P. Xavier, J. Canny, J. Reif https://www.cs.duke.edu/brd/papers/src-papers/jacm-final.pdf The authors present a PTAS algorithm that can ...
15
votes
2answers
813 views

Does Karp reducibility yield a total order?

Or with other words, do we have that for every language $A$ and $B$, $A \leq_p B$ or $B \leq_p A$?
6
votes
1answer
127 views

Equivalence for Constant-width Read-Once Branching Programs with Distinct Orders

Let $X={x_1,...,x_n}$ be a set of variables and $\pi:[n]\rightarrow [n]$ be a permutation of the $n$-element set $[n]=\{1,...,n\}$. A $\pi$-OBDD is an oblivious, read-once branching program where ...
0
votes
1answer
127 views

Why are these two definitions of PLS equivalent?

In the definition of the complexity class $\textsf{PLS}$ we have an algorithm for improving the solutions locally. I have come across the following two definition of such an algorithm. there is a ...
9
votes
1answer
371 views

2-NEXPTIME-complete problems

We have a problem and we found an algorithm that appear to be 2-nexptime. I would like to find known 2-nexptime-complete problems in order to find a lower bound. I found in literature mainly two ...
5
votes
1answer
157 views

Complexity of counting maximum number of co-linear points in Euclidean plane

The problem: given a set of points in the Euclidean plane, find the maximum number of co-linear points. I already know that the problem can be solved in quadratic time using hashing or projective ...
4
votes
0answers
126 views

Natural Problems NSPACE[n] but not in DTIME[n]

It is known that $\mathrm{DTIME}[n]\subseteq \mathrm{DSPACE}[n/\log n]$. Therefore, there are languages in $\mathrm{DSPACE}[n]$ which are not in $\mathrm{DTIME}[o(n\log n)]$. Are there examples of "...
10
votes
1answer
231 views

EXP-Complete Problems vs Subexponential Algorithms

Does the fact that a problem $A$ is EXP-time complete implies that $A$ is not in $DTIME(2^{o(n)})$? I'm aware that by the time hierarchy theorem, $EXP=DTIME(2^{n^{O(1)}})$ is not included in $E=...
6
votes
0answers
113 views

Complexity of validity of first-order logic over finite words with bounded quantifier alternation?

I'm concerned with the validity problem for sentences of first-order logic over finite words, i.e. $FO[\le]$ interpreted over finite subsets of $\mathbb{N}$. AFAIK it should be nonelementary. However,...
10
votes
1answer
364 views

Status of PP-completeness of MAJ3SAT

SHORT QUESTION: Is MAJ-3CNF a PP-complete problem under many-one reductions? LONGER VERSION: It is well-known that MAJSAT (deciding whether the majority of assignments of propositional sentence ...
0
votes
1answer
183 views

obvious property of big O, big Omega, and big Theta [closed]

I'm trying to determine under what conditions the following statement is true. The statement is, suppose $f(n) = O[g(n)]$ and $f(n) \neq \Theta[g(n)]$ then $g(n) = \Omega[f(n)]$ where $O$ means "...
6
votes
1answer
192 views

Number of solutions for a system of linear equations over a finite ring

Let $R$ be a finite ring with operations $(+,\cdot)$. Let $A \in R^{m\times n}$ and $b\in R^{m}$. Questions: What is the complexity of counting the number of solutions to the system of equations $...
5
votes
1answer
392 views

How is the VP=VNP question in char 2 different from other char? What is the current frontier in regards to this question?

What are the caveats one should be aware of when pursuing VP=VNP question in char 2 compared to other char? What is the current frontier in regards to this question?
14
votes
2answers
333 views

Collapses under the assumption that $NEXP\subseteq P/Poly$

It is known that if $NP\subseteq P/Poly$ then the polynomial hierarchy collapses to $\Sigma_2^{P}$ and $MA = AM$. What are the strongest collapses known to happen if $NEXP\subseteq P/Poly$?
-2
votes
1answer
175 views

A variant of the Post Correspondence problem

Given words $\alpha_1, \ldots \alpha_n$ and $\beta_1, \ldots, \beta_n$, Post's Correspondence Problem asks if there is a sequence $i_1, \ldots, i_k$ of indices such that $\alpha_{i_1} \ldots \alpha_{...
10
votes
3answers
504 views

P/Poly vs Uniform Complexity Classes

It is not known whether NEXP is contained in P/poly. Indeed proving that NEXP is not in P/poly would have some applications in derandomization. What is the smallest uniform class C for which one can ...
4
votes
1answer
81 views

Complexity of propositional LTL with past operators and freeze quantifier?

In "A Really Temporal Logic", by R.Alur and A.Henziger, they introduce an extension of Linear Temporal Logic with a freeze quantifier $x.\phi$, which allows to "give a name" to the current time point ...
1
vote
0answers
81 views

Complexity of Maximum Independent Set (or Vertex Cover) on disk packing graphs

I'm interested in complexity results for Maximum Independent Set (or Vertex Cover) problem over the class of disk packing graphs. Having a set of disks we build a graph that has its vertices at the ...
-1
votes
0answers
109 views

Complexity of enumerating all k-cliques in a k-partite graph

Can someone explain to me or point me to any references discussing the complexity of enumerating all k-cliques in an unweighted k-partite graph? For example, what is the complexity of enumerating all ...
6
votes
1answer
352 views

What is the complexity of vertex cover on k-partite graphs?

Given a k-partite graph which is already partitioned into k parts, what is the complexity of finding a vertex cover of minimum size? I guess that it's NP-hard, but couldn't yet prove it or find ...
1
vote
0answers
57 views

Equivalent SDP problems different solving times

I have two SDP problems which are proved to be equivalent (in terms of optimal objective values) to each other in theory. Moreover, they have same number of constraints and variables respectively. ...
2
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0answers
185 views

Circuit complexity lower bounds and uniformity

I have troubles to understand how lower bounds w.r.t. circuit complexity and upper bounds w.r.t. uniform machine models can be used to show completeness results. For example, the word problem for ...
1
vote
0answers
647 views

Is there any theory that allows to compute the computational complexity boundaries like this?

I recently had an interview, at which I was asked to solve the following problem: you have a sorted array of integers, and you need to find if there are 3 numbers that sum to 0. The brute force ...
0
votes
2answers
395 views

NP completeness of linear $0-1$ assignment problem

Supposing we have a linear equation in $n^2$ variables with integer (negatives allowed) coefficients of at most $m$ bits each. Partition $\Pi_1$ the variables into $n$ disjoint sets of $n$ variables ...
1
vote
1answer
97 views

What's a good advanced textbook/resource for studying the complexity of counting and combinatorics?

I'm taking a class in enumerative combinatorics. The professor focusses on the complexity of solving combinatorics problems like partitions etc. I'm using Enumerative Combinatorics but it does not ...
1
vote
1answer
94 views

“Checking equality for Kolmogorov complexity of two sequences” is computable?

It is a known result that Kolmogorov complexity is not computable for every arbitrary sequence. I wonder whether the following problem is computable or not: "Given $x$ and $y$ as two sequences, ...
2
votes
0answers
48 views

Is there any exsiting research on this kind of “sorting with constraint” problem?

I have been interested in this kind of "sorting with constraint" problem: Given $n$ items $\{S_1 ,S_2 ,...S_n\}$ with corresponding weight $w_i ,i=1,2,...,n$, we want to sort these $n$ items (i.e. ...
3
votes
1answer
443 views

Computational complexity of modular power towers (tetration)

The complexity of modular addition is known: $g + p \mod N$ (for $|p| \approx |g| \approx |N|$) can be computed in $O(n = |N|)$. The complexity of modular multiplication is open though some results ...
6
votes
1answer
128 views

Is the computation of a satisfying variable assignment for a Boolean formula $FP^{NP}$-hard?

By the well-known self-reducibility of SAT we can obtain a satisfying variable assignment for a Boolean formula by a polynomial number of calls to an $NP$ oracle (delivering only yes/no answers). Thus,...
1
vote
2answers
185 views

Complexity analysis on a parameterized recurrence relation

In order to analyse the complexity of our algorithm, we try to solve this recurrence: $T(n)=3T(n-1)-T(n-2)+T(n-k)+3^k$ ; in which $k$ is a parameter to be fixed. We know that this kind of ...