Questions tagged [cc.complexity-theory]

P versus NP and other resource-bounded computation.

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Is Hankelability NP-hard?

I asked this question on SO on April 7 and added a bounty which has now expired but no poly time solution has been found yet. I am trying to write code to detect if a matrix is a permutation of a ...
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Counting Isomorphism Types of Graphs

Polya's counting theorem leads to an algorithm for counting (precisely) the number of isomorphism types of graphs with $n$ vertices in $\exp (\sqrt n )$ steps. From Polya theorem you get a formula ...
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Fine-grained complexity of BPP

If E does not have i.o.-$2^{o(n)}$ circuits, then P=BPP, but this does not tell us about the fine-grained containments between $\mathrm{Time}(n^a)$ and $\mathrm{BPTime}(n^b)$. Are there reasonable ...
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What is the power of general poly-size permutation branching programs?

Call $\mathsf{PPBP}$ the class of languages decided by poly-size families of permutation branching programs, which are layered branching programs (i.e., the ones defined here) whose transitions ...
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Descriptive complexity characterization of TimeSpace classes

Are there descriptive complexity characterizations for TimeSpace complexity classes like $\mathsf{SC^i}= \mathsf{DTimeSpace}(n^{O(1)},O(\lg^i n))$?
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Partial circulant matrices: Is there a non-zero vector $v\in \{-1,0,1\}^n$ such that $Mv=0$?

The following question arose as a side product of some work I have been part of recently. An $m$ by $n$ $(0,1)$-matrix $M$ is partial circulant if it can be formed by taking the first $m$ rows of a ...
437 views

Interesting PCP characterization of classes smaller than P?

The PCP theorem, $\mathsf{NP} = \mathsf{PCP}(\mathsf{log}\, n, 1)$, involves probabilistically checkable proofs with polynomial time verifiers, so the smallest class that can be characterized in this ...
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Complexity of finding the smallest well-covered completion

This is related to an earlier question on which graphs have the property that all maximal independent sets are maximum — such graphs turn out to be known as the well-covered graphs. Any graph $G$ is ...
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What is the evidence for average case separation between EXP and NEXP?

There is significant evidence from cryptography that there exist NP-complete problems that are hard in the average case (meaning that e.g. $AvgP \nsupseteq DistNP$). Namely, we have candidate one-way ...
441 views

Is graph coloring complete for poly-APX?

Is the graph coloring problem complete for poly-APX under C-reductions (alternatively, under AP-reductions)? For the graph coloring problem, speaking of a feasible solution means a proper coloring for ...
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Is Node Multiway Cut NP-complete on planar graphs when all terminals lie on the outer face?

I am interested in the following problem. Node Multiway Cut on Planar Graphs with terminals on the outer face Instance: A plane graph G, and integer k, and a set $S \subseteq V(G)$ of terminals ...
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An algebra of complexity classes

A key feature of unrelativized computation is its composability out of smaller fragments, and to partially capture the composability, I came up with an algebra of fine-grained complexity classes. For ...
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Complexity of approximating the range of a matrix

Given an $m$ by $n$ matrix $M$ with $m \leq n$ and elements from $\{-1,1\}$, let us define: $$S_M = |\{Mx : x \in \{-1,1\}^n\}|.$$ I believe that it is NP-hard to compute $S_M$ exactly, by applying ...
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Williams' Method, Natural Proofs and Constructivity

I have some questions on the previous question which is written bellow. Natural Proof and Constructivity : The topic of the previous question Recently, Ryan Williams proved that Constructivity in ...
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First use of sans serif for complexity classes

(Apologies for the triviality of this question; nevertheless, it's been bugging me and presumably people here will be able to answer it...) It seems that it has become popular in recent years to ...
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The best known upper bound for two-way probabilistic finite automata with one-counter

It is known that the class of languages recognized by two-way deterministic finite automata with one-counter (2D1CAs) is a proper subset of $\mathsf{L}$ (deterministic log-space): A 2D1CA can run at ...
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Pseudorandom functions in ACC^0?

In the lower bound result by Ryan Williams (Non-uniform $\mathsf{ACC}$ circuit lower bounds), there is a mention of "little evidence that Pseudorandom function generators exist in $\mathsf{ACC}^0$. Is ...
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AC0 many-one reduction of Mod_3 to PRIMES?

Let Mod$_3$ be the language of binary strings with the sum of the bits divisible by 3, and PRIMES be the set of prime integers. In a 2001 paper A Lower Bound for Primality, Allender, Saks, and ...
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DPLL and Lovász Local Lemma

Let $\varphi$ be a CNF formula. Suppose that each of $\varphi$'s clauses consist of exactly $t$ literals (and, moreover, all literals within one particular clause correspond to different variables). ...
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Question on Products of Graphs

Let $S_{n}(G)$, $C_{n}(G)$, $T_{n}(G)$ be the $n$-fold Strong Product, Cartesian Product and Tensor Product of a graph $G$ on $|V|$ vertices. Let the chromatic number ($\chi(G)$) and the independence ...
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Linear PRAM vs Arithmetic Linear PRAM

A linear PRAM model is a PRAM model without bit operations and at least one operand of the $\times$ instruction is a constant. If in addition we require that the running time does not depend on the ...
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Any example of an unsatisfiable integer program with non constant Rank Lower bounds for LS+ cuts but with short LS+ refutations?

Assume we want to refute an unsatisfiable CNF. We can interpret it as an integer program, thus a refutation can be done by applying Lovasz-Schrijver semidefinite cuts ($LS_{+}$ cuts) to its linear ...
$\mathsf{DLogTime}$ and $\mathsf{NLogTime}$ are two of the smallest complexity classes we have. (Note that logarithmic time hierarchy $\mathsf{LH}$ is equal to $\mathsf{AC}^0$ and these are the first ...