# Tagged Questions

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### Is there a natural problem in quasi-polynomial time, but not in polynomial time?

László Babai recently proved that the Graph Isomorphism problem is in quasipolynomial time. See also talk at University of Illinois, Chicago, note from the talks by Jeremy Kun GLL post 1, GLL post 2,...
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### What is the status of intermediate problems if P is not NP in worst way imaginable?

Assume $P\neq BPP\neq NP$ with caveat that there is a deterministic algorithm for every $NP$ complete problem with input size $n$ bits in $2^{(\log n)^{1+f(n)}}$ arithmetic operations on $\log n$ ...
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### Is any QMA-intermediate problem known?

Similar to the class of classical NP-intermediate problems (e.g. Graph Isomorphism), is there any "QMA-intermediate" problem known, that is in QMA but not known to be QMA-complete? Has this been ...
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### Is $P^{NPI}$ different from $P^{NP}$?

Can we prove that for every language $L\in\mathsf{NP}$ that is not $\mathsf{NP}$-hard (this assumes $\mathsf P \ne \mathsf{NP}$), $\mathsf{P}^L \ne \mathsf{P}^{\text{SAT}}$? Alternately, can this be ...
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### Why are so few natural candidates for NP-intermediate status?

It is well known by Ladner's Theorem that if ${\mathsf P}\neq \mathsf {NP}$, then there exist infinitely many $\mathsf {NP}$-intermediate ($\mathsf{NPI}$) problems. There are also natural candidates ...
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### Techniques for showing that problem is in hardness “limbo”

Given a new problem in $\mathsf{NP}$ whose true complexity is somewhere between $\mathsf{P}$ and being NP-complete, there are two methods that I know of that might be used to prove that resolving this ...
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### Are there “NP-Intermediate-Complete” problems?

Assume P $\ne$ NP. Ladner's Theorem says that there are NP Intermediate problems (problems in NP that are neither in P nor NP-Complete). I have found some veiled references online that suggest (I ...
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### Complexity class of this problem?

I am trying to understand to which complexity class the following problem belongs: Exponentiating Polynomial Root Problem (EPRP) Let $p(x)$ be a polynomial with $\deg(p) \geq 0$ with coefficients ...
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### GI-hard graph problem not known to be $NP$-complete

Graph Isomorphism ($GI$) is good candidate for $NP$-intermediate problem. $NP$-intermediate problems exist unless $P=NP$. I'm looking for natural problem that is hard for $GI$ under Karp reduction (A ...
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### Natural candidates for the hierarchy inside NPI

Let's assume that $\mathsf{P} \neq \mathsf{NP}$. $\mathsf{NPI}$ is the class of problems in $\mathsf{NP}$ which are neither in $\mathsf{P}$ nor in $\mathsf{NP}$-hard. You can find a list of problems ...
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### 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 ...
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### Why are NPI problems not all of the same complexity?

How does one look at a problem and reason that it is likely NP-Intermediate as opposed to NP-Complete? It is often pretty simple to look at a problem and tell whether it is likely NP-Complete or not ...
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### NP-intermediate problems with efficient quantum solutions

Peter Shor showed that two of the most important NP-intermediate problems, factoring and the discrete log problem, are in BQP. In contrast, the best known quantum algorithm for SAT (Grover's search) ...