# Questions tagged [complexity]

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### proving that a problem is in P [migrated]

I read online that this problem is in P: Problem = {a^n, where n is a primary number} I can't find any algorithm that decides if a word w in ...
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### Is 4-Coloring restricted to graphs with crossing number 1 NP-complete?

Planar graphs are 4-colorable. Determining if a planar graph is 3-colorable is NP-Complete. A graph with a crossing number 1 (graph such that it can be drawn with $\le 1$ crossing) is 5-colorable. ...
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### Sentences in what kinds of grammar in the Chomsky hierarchy can be parsed by an LSTM of a given size?

Given an LSTM $N$ of a given size $A$, a sentence $S$ with a given number of words $B$, a Chomsky grammar hierarchy level $C$ in 0-3, a Chomsky grammar $G$ of level $C$ of size $D$, A given fixed, ...
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### Looking for Research in Cryptographic Computing

I recall reading in college about a nascent research area regarding cryptographic techniques for secure computing, relating to zero-knowledge proofs, but I am having trouble remembering the exact term....
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### 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 ...
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### 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 ...
359 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 ...
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### 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 ...
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### 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 ...
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### 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,...
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### 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 ...
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 "...