Questions tagged [p-vs-np]

Questions about or related to P vs. NP

16 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
320 views

What would be the consequences if all _infinite_ NP-complete languages are p-isomorphic?

The famous Isomorphism Conjecture of Berman and Hartmanis says that all $NP$-complete languages are polynomial time isomorphic ($p$-isomorphic) to each other. It has been an early attempt (published ...
503 views

Assigning probability to membership in an NP-complete language

Motivation Assuming $\mathsf{P}\ne\mathsf{NP}$, it is impossible to efficiently decide membership in an NP-complete language. I would like to assign probability to such membership, in some sense. ...
256 views

Are there sampNP-intermediate problems?

I approximately copied the brief "introduction" to average-case complexity theory of NP from my previous question. However, this question is completely different, so please read on It is conjectured ...
168 views

332 views

Can Category Theory help us prove P != NP?

Scott Aaronson, in this funny April Fools’ Day post, introduces a fictionalized $P \neq NP$ Proof and, among other things, he says that the proof make use of Higher topos theory to solve the biggest ...
125 views

What are some known methods for showing that a class has no complete problems?

The only way that I know of is the way that you can show that $RE \cap coRE$ does not via diagonalization. Mostly curious because if $NP \cap coNP$ has no complete problems then $P \neq NP$. I tried ...
124 views

What would faster Fourier Transform(FFT?) and/or multiplication algorithms imply?

There are many problems which have implications on P vs. NP and other complexity classes. Supposing that we're interested in Fourier transforms and/or multiplication algorithms, do faster Fourier ...
388 views

What's the Impact if proven NP/co-NP=PSPACE on settling P=NP? The future directions it opens to settle/attack P=NP? Remaining classes left outside?

The primary Impact i know would be that: Polynomial Hierarchy collapses to Level 1. NP=co-NP NP=BPP NP=PSPACE BQP=NP and so on.. What are the attack directions it will open for settling P=NP (in ...
339 views

intuition that VP=?VNP is (not?) connected to P=?NP

recently there has been major progress into the VP=?VNP problem for algebraic circuits originated by Valiant, inspiring some optimistic outlook on its eventual or imminent resolution. what is an ...
149 views

What is known about lower bounds on the algorithm if P=NP

I recall Scott Aaronson making the claim that either $P\neq NP$ or he has superpowers. What reason is there, if any, to believe that it is not the case that any decision procedure has constants (or ...
What are the consequences of a ${\bf O}$(m) algorithm for SAT
We are given a Boolean formula $F$ in conjunctive normal form with $n$ variables and $m$ clauses and we would like to know if there exists at least one assignment to the $n$ variables that makes $F$ ...
According to the answers in posting it is possible that $\mathsf{VP} = \mathsf{VNP}$ and $\mathsf{P} \neq \mathsf{NP}$ are simultaneously correct. $\mathsf{VP} = \mathsf{VNP}$ implies \$\mathsf{P/...