# Questions tagged [cc.complexity-theory]

P versus NP and other resource-bounded computation.

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### DFSA and NFSA intersection problem

Given $k$ deterministic FSAs of $n$ states the intersection of their languages is empty is decidable in $n^{o(k)}$ time is an open problem. For unbounded $k$ it is known the problem is $PSPACE$ ...
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### Improving the approximation in Stockmeyer's counting theorem

Given a $\#P$ function $f(x)$, we can use Stockmeyer's counting theorem to get an approximation $g(x)$ such that \begin{equation} \left(1 - \frac{1}{\text{poly}(n)} \right) f(x) \le g(x) \le \left(...
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### Amortized time and worst case (non-amortized) separation

Assume a reasonable computation model (thinking about pointer machine or RAM model), is there a problem where there is a clear separation between amortized and worst case complexity? Say, if ...
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### $CH=UL$ and partial breaking of transitive closure bottleneck problem and Savitch's theorem?

Let $L^t=DSPACE[O(\log n)^t]$, $NL^t=NSPACE[O(\log n)^t]$ and $UL^t=USPACE[O(\log n)^t$. Savitch provides $NL\subseteq L^{2}$. If $CH=UL$ we clearly got rid of the transitive closure bottleneck ...
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### A proved computationally-irreductible function

In arXiv:1111.4121 and arXiv:1304.5247, Hervé Zwirn and Jean-Paul Delahaye propose a formal definition of computational irreducibility. Is there a (possibly artificial) function that can be proved to ...
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### What is the best simulation of majority utilizing $\bmod\{2,3,\dots,p\}$ gates?

It is known $AC^0$ cannot get majority function. Is there a literature on simulation of $MAJ$ function utilizing $AC^0[2,3,\dots,p]$ gates for a finite fixed set of primes $2$ to $p=O(1)$? What is ...
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### Is $GCT$ necessarily a negative result program?

$GCT$ is a candidate program to separate permanent and determinant through symmetries. If indeed permanent and determinant can be handled in similar complexity class would $GCT$ be a program which can ...
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### Algorithms for finding unique solutions of NP-complete problems

The complexity of algorithms that find unique solution for an NP-complete problem (the input is guaranteed to have a unique solution) seems to shed light on the hardness character of different NP ...
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### Pursuing Theoretical Computer Science after CS major

So I am currently a sophomore majoring in Computer Science. In the Data Structures course that I am currently studying, I studied the basics of complexity of a program and big O-notation, etc. That ...
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### Is the Triangle Finding decision problem in $coNTIME(\tilde{O}(n^2))$?

The Triangle Finding decision problem asks whether there exists a triangle in a graph $G$ containing $n$ vertices. A triangle is a triple of vertices $(a, b, c)$ such that $a$ is adjacent to $b$, $b$ ...
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### The graph of problem reductions

A classical approach to study the complexity of a problem $P$ is to efficiently reduce a well known problem $P'$ to $P$, thus showing that $P$ is at least as difficult as $P'$. The TCS literature ...
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### PSPACE-complete under NP reduction

Is there some example of a PSPACE problem that we can show PSPACE-hard under NP reduction, but we do not know a proof of PSPACE-hardness under P reduction ? To be more precise, the NP reduction I am ...
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### Clauses structure as quenched random matrix for random $k$-SAT problems

In the Section III of Statistical mechanics of the random K-SAT model, the clauses structure of random $k$-SAT problems are expressed as $M \times N$ quenched random matrix where the numbers of ...
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### Which algorithm for linear programming is suitable for the context of quantum computing?

There are two major types of algorithms for linear programming : extreme point based, interior point based. Which will be suitable for quantum computing?
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### Relationship between SC and NL

It is a major open problem whether $NL \subseteq SC$, or equivalently, whether directed reachability can be solved (simultaneously) in poly-logarithmic space and polynomial time. What is known ...
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### Size of CNF Formula for Adjacency in Configuration Graph

Suppose $M$ is a (non-deterministic) TM that runs in space $S(n)$. Then, the configuration graph $G_{M,x}$ of $M$ on $x$ has size $2^{O(S(n))}$. Arora-Barak (see http://theory.cs.princeton.edu/...
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### Looking for some lecture videos on logic, models of computation and computational complexity/tcs fundamentals [closed]

Looking for some lecture videos (introductory level) on logic, models of computation as well as computational complexity/ other theoretical computer science fundamentals
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### Living in Minicrypt, but sampling hard instances without the solution

In Impagliazzo's worlds, Minicrypt is the one, where one way functions exist. In other words, we can sample hard-on-average instances of NP complete problems. Question: Is living in Minicrypt, where ...
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### Complexity of a satisfiability problem

I would like the know the complexity of a specific satisfiability problem. I have a feeling it could be solved in polynomial time, but I am not sure about it. The problem is described below. Given $n$ ...
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### Complexity of MAX-ONEs Monotone 2-SAT with $n^{3/2}$ or $C n^2$ clauses?

Let $\phi$ be negative monotone 2-CNF on $n$ variables and $n^{3/2}$ clauses. What is the complexity of finding satisfying assignment with maximum number of ones $k$? Alternatively let $G$ be a graph ...
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### Why does Dinur's proof of the PCP theorem fail to work for unique games?

What is the critical step where things go wrong if one attempts to use Dinur's proof the PCP theorem to prove the unique games conjecture by starting from a unique label cover instance and doing gap ...
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### Some examples of tools to demonstrate problem is in $NC$ [closed]

Unlike the class $P$ or $NP$ the class $NC$ does not have any complete problems. To show a problem is in $NC$ one needs to marshal efforts to directly show the problem is in $NC$ since there are no ...