Questions tagged [nexp]
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24 questions
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How do we show directly coNP is in MIP?
I know one can show that by $\mathsf{coNP}\subseteq\mathsf{NEXP}=\mathsf{MIP}$. But here I would like to start with a $\mathsf{coNP}$-complete problem and show there is a two-prover one-round ...
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2
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Best known algorithm for NEXP-complete problem
What is the best (in time) algorithm for NEXP-complete problems?
Is there an algorithm that solve a NEXP-complete problem in time $2^{o(2^n)}$?
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2
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Why should we believe that $NEXP \not \subset P/poly$
I am sorry if this is not an advanced question. Most computer scientists believed that $NEXP \not \subset P/poly$ but they are not even close to this assumption. The main evidence that they are used ...
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CNF encoding of set cover - NExpTime-completness
Notation: given a CNF formula A over variables X, we write $[A(X)]$ for the set of valuations $v: X \to \{0,1\}$ such that $A(X/v)$ is true, i.e. the set of valuations that makes formula A true.
I ...
2
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1
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Is it possible to reduce an NP language to a NEXP language with exponentially smaller input length?
Suppose we have an NP-complete language $L_1$ and a NEXP-complete language $L_2$.
For any deterministic exptime machine $M_1$ with oracle access $M_1^{L_1}$, is it possible to find a deterministic ...
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4
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1
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330
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Results comparing BQP and NEXP
Are there oracle results with $$P=NP\neq BQP=NEXP\mbox{ and }P=NP\neq BQP\neq NEXP?$$
Also is there a $PCP$ characterization of $BQP$ like $$PCP(O(poly(n)),1)=PCP(O(poly(n)),O(poly(n)))=NEXP?$$
- 13.8k
2
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A question about UE
Much has been written about the class UP see related (even more in literature)
example question here. Much is understood about the class UP, and its place in collapsing the PH too. UP has a played ...
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9
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1
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Indications that strengthen the conjecture: NEXP ⊊ EXP^NP
I am trying to find indications that strengthen the conjecture of NEXP ⊊ EXP^NP.
Clearly NEXP ⊆ EXP^NP, and there are some hints that this inclusion is proper.
Some Examples:
1. A paper by Shuichi ...
- 1,656
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Solving 0/1 integer programming and solving ACC-of-SYM circuits
I am referring to the proof of Theorem 1.4 in this STOC 2014 paper, https://arxiv.org/abs/1401.2444. In particular my question is about the argument that begins in the 8th line of page 9 where the ...
- 1,483
6
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On succinct $EXP$ and $NEXP$ complete problems?
We know succinct version of many $P$-complete problems are $EXP$-complete. There are standard ways to define $EXP$-complete graph problems from succinct representations of these $P$ complete problems. ...
- 13.8k
2
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Are there non-trivial MIP protocols with initially-independent verifiers?
My impression is that for standard constructions of MIP ("Multiple Independent Prover") protocols, the verifiers must have shared randomness. What happens if the verifiers are
also independent ...
user6973
9
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1
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678
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Complexity of validity problem for Monadic First Order Logic?
Monadic First Order Logic is FOL with no function symbols, and predicate symbols restricted to arity 1. For this question, let's say that the = symbol is also forbidden. I want to know the complexity ...
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491
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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 ...
- 2,201
10
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Is there a counting complexity class for succint problems?
Encoding NP-complete problems succintly often makes them NEXP-complete. I am wondering if counting the number of solutions to such a problem with a succint encoding would be any harder than solving ...
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14
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775
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NEXPTIME-completeness with more time for reductions
One thing that surprised me when learning about complexity theory is that for a complexity class C, we tend to define C-complete using polynomial time reductions, even when C is a very large ...
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