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Questions tagged [cc.complexity-theory]

P versus NP and other resource-bounded computation.

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Parsimonious Reduction from Unique-3SAT to NAE-3SAT

Using the result by Valiant and Vazirani, we know that Unique-3SAT (3SAT with a unique solution) is hard unless NP=RP. Also it is widely believed that the "Unique" version of any NP-complete problem ...
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Interesting variation to the subset sum problem

An interesting variation of the subset sum problem was presented to me by a friend from work: Given a set S of positive integers, of size n, and integers a and K, is there a subset R (of the set S) ...
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Sorting with an average of $\mathrm{lg}(n!)+o(n)$ comparisons

Is there a comparison-based sorting algorithm that uses an average of $\mathrm{lg}(n!)+o(n)$ comparisons? Existence of a worst-case $\mathrm{lg}(n!)+o(n)$ comparison algorithm is an open problem, but ...
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Fast classical simulation of quantum algorithms

Are there examples of cases where the classical simulation of a quantum algorithm for a problem outperforms the best previously known classical algorithm for this problem? "Outperforms" doesn't have ...
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Example demonstrating the power of non-deterministic circuits

A non-deterministic Boolean circuit has, in addition to the ordinary inputs $x = (x_1,\dots,x_n)$, a set of "non-deterministic" inputs $y=(y_1,\dots,y_m)$. A non-deterministic circuit $C$ accepts ...
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Reasoning about NP hardness of optimization problems with closed form functions as input

(This may not be a research level question per se. I can delete this question if the community thinks this way too) I am trying to understand how to reason about hardness of optimization problems ...
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Is Norbert Blum's 2017 proof that $P \ne NP$ correct?

Norbert Blum recently posted a 38-page proof that $P \ne NP$. Is it correct? Also on topic: where else (on the internet) is its correctness being discussed? Note: the focus of this question text has ...
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Conesequences of $\forall k\in \mathbb N \space NP\not\subseteq TISP(poly(n),n^k)$

Does $\forall k\in \mathbb N \space NP\not\subseteq TISP(poly(n),n^k)$ has any separation of classes or consequences? My main question is can use this to show that $P \neq NP$ or some thing useful ...
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Understanding the definition of a “restriction of a resolution derivation”

I am reading the paper An Introduction to Lower Bounds on Resolution Proof Systems. In its subsection 2.3 the author gives an inductive definition of the restriction of a resolution refutation $\pi$. ...
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Why is it a mystery if PSPACE ?= EXPTIME?

It seems obvious to me that $PSPACE \neq EXPTIME$. I, however, do not believe that my seemingly obvious logic would not be picked up by more intelligent people if it was so simple, so I'm assuming ...
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Is the following optimization problem (another variant to a previous problem) NP-hard?

This problem is a following up question on this one. The only difference is the addition of $3^{rd}$ constraint "$\sum_{i} x_{ij} \le M$", where M is a constant number. This constraint essentially ...
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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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NP completeness of Hamiltonian cycle for the family of *dual graphs* to plane, cubic, triply connected graphs?

It is well known that the Hamiltonian cycle problem is NP-complete on the family of planar, cubic and triply connected graphs: https://epubs.siam.org/doi/abs/10.1137/0205049 For a problem I'm ...
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Is there a polynomial time algorithm to determine if the span of a set of matrices contains a permutation matrix?

I would like to find a polynomial time algorithm that determines if the span of a given set of matrices contains a permutation matrix. If any one knows if this problem is of a different complexity ...
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Is $\textbf{BPP} \subseteq \textbf{P}^{\textbf{NP}}$?

Is it known that $\textbf{BPP} \subseteq \textbf{P}^{\textbf{NP}}$?
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Is this game EXPSPACE-complete?

Let $M$ be a polynomial-time deterministic machine that can ask questions to some oracle $A$. Initially $A$ is empty but this is can be changed after a game that will be described below. Let $x$ be ...
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Does there exist a polynomial time algorithm to determine whether an equation is a consequence of (x+y)*(y+z)=(x*y)+(y*z)?

Consider the identity $C$ $$(x+y)\times(y+z)=(x\times y)+(y\times z).$$ Is the problem of determining whether an identity is a consequence of $C$ in universal algebra a polynomial time problem? This ...
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Sorting a programs instructions until it works

Lets say I have a computer program below. (define (factorial x) (if (= x 0) 1 (else (* x (factorial (- x 1))))) I then take each line of the ...
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Pseudodeterministically choosing elements from efficiently samplable distributions (or, the plausibility of a weak choice principle)

Suppose we have a poly-time samplable family of distribution. I.e., a family of distributions $D_n \subseteq \{0, 1\}^{\mathsf{poly}(n)}$ and an algorithm $S$ for which $D_n = (r \leftarrow^\$ \{0,1\}^...
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Ruzzo-Simon-Tompa oracle access mechanism

In a paper on relativizing logspace computations, Ladner and Lynch construct an oracle relative to which $\mathsf{NL} \nsubseteq \mathsf{P}$. There are some more pathological examples in this vein in ...
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Inapproximability of multiterminal cut

In the multiterminal cut the input is a graph $G$ and a subset $T$ of its vertices. The task is to remove the minimum number of edges from $G$ such that there is no path connecting any distinct ...
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Distributions which are intractable to sample from?

I'm looking for an interesting family of probability distributions $P$ that is intractable to efficiently sample from. I'm not sure what the right notion of intractable is, though I know the notion ...
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What is best known space requrement for solving SATISFIABILITY problem in exp time

I searched a lot for finding best space requirement algorithm for SATISFIABILITY problem but I didn't find any thing better than brute force that is in DSPACE(n). is there exists better bound? and ...
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Problems in BQP but conjectured to be outside P

Wikipedia listed four problems that are in $BQP$ but conjectured to be outside $P$: Integer factorization; Discrete logarithm; Simulation of quantum systems; Computing the Jones polynomial at certain ...
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Deciding whether an interval contains a prime number

What is the complexity of deciding whether an interval of the natural numbers contains a prime? A variant of the Sieve of Eratosthenes gives an $\tilde O(L)$ algorithm, where $L$ is the length of the ...
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Max cut problem between two connected subgraphs

Let $G$ be a connected graph. Consider the problem of finding a partition $G = A \cup B$ into connected subgraphs, so that the cut between $A$ and $B$ is maximized. Is there anything which is known ...
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What does “hold uniformly” mean in the context of asymptotic analysis?

What does "hold uniformly" mean in the statement of Theorem 1.7 in A Faster Subquadratic Algorithm for Finding Outlier Correlations? Here's the theorem text ("hold uniformly" is in the last line):
Apologies for a simple question - I am a beginning graduate student in TCS. Consider the following $\mathrm{ExactCover}$ problem: Given a collection $\mathcal{S}$ of subsets of a universe set $U$ and ...
The question is: given a planar graph $G$ with unit capacity edge weights and a fixed positive integer $k$, what is an approximation algorithm for finding the minimum size of a cut $(A,B)$ with $|A|=k$...