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Questions tagged [np-intermediate]

13 questions
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NP-complete problem with a polynomial number of yes-instances?

I have the impression that for every NP-complete problem, for infinitely many input sizes $n$, the number of yes-instances over all possible inputs of size $n$, is (at least) exponential in $n$. Is this true? Can it be proven (probably only under…
Albert Hendriks
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Are NP-complete sets formed from two other sets only if at least one is NP-hard?

This question is somewhat of a converse to a previous question on sets formed from set operations on NP-complete sets: If the set resulting from the union, intersection, or Cartesian product of two decidable sets $L_1$ and $L_2$ is NP-complete, is…
Ari
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Constructing languages in NPI other than through Ladner's Theorem

I have seen proofs of Ladner's theorem which detail the construction of languages in NPI assuming P $\neq$ NP. However, I was wondering if there are any other constructions using the fact that sparse sets cannot be NP-complete assuming P $\neq$ NP…
Ari
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Complete problems in NP∩coNP

I often read in Complexity literature that NP∩coNP is unlikely to have any complete problems. Is that unlikelihood "proved" ? By proved, I mean that there would be a theorem that would relate the existence of such a problem to, by instance, the…
wazdra
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Assuming that $P \neq NP$, show that there exist sets $A$ and $B$ in $NP$ such that neither $A \leq _T^p B$ nor $B \leq _T^p A$

My question is as follows: Assuming that $P \neq NP$, show that there exist sets $A$ and $B$ in $NP$ such that neither $A \leq _T^p B$ nor $B \leq _T^p A$, where $A \leq _T^p B$ if there exists a polytime deterministic oracle machine that computes…
Slugger
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Is there a notion similar to NP-intermediate, but for higher classes in PH?

It is well-known that (assuming P$\neq$NP), there are problems in NP that are not NP-hard neither in P. Such class of problems are called NP-intermediate (https://en.wikipedia.org/wiki/NP-intermediate), and one candidate problem that might be…
441Juggler
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Is this an example of a natural, strictly NP-intermediate language (assuming EXP ≠ NEXP)?

In the wikipedia page for the NP-intermediate complexity class, the following observation is made: Under the assumption that P ≠ NP, Ladner explicitly constructs a problem in NPI, although this problem is artificial and otherwise uninteresting. It…
Federico
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Is there a comprehensive list of complexity theoretic reductions from and to prime number factorization?

I am interested in the complexity theoretic equivalences of prime number factorization. My interest stems from prime number factorization being one of the few candidates for NPI. I am especially interested to learn wether there are some not…
ckrk
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Assuming NP≠coNP, do we have a similar theorem to Ladner's?

We have that $\mathrm{NP\neq coNP\iff NP\neq NP\cap coNP}$. So by assuming that $\mathrm{NP\neq coNP}$, can we prove the existence of intermediate problem between $\mathrm{NP}$-complete and $\mathrm{NP\cap coNP}$?
user92914
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Is following observation on Ladner's theorem correct?

Suppose $NP\subseteq DTIME[n^{f(n)}]$ where $f(n)$ is any function satisfying $\omega(1)$ then is it true $P=NP$ holds? Ladner's theorem states infinite time hierarchy between $P$ and $NP$. That is there are $NP$ problems in $DTIME[n^{g(n)}]$ for…
Turbo
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Do all P problems reduce to all NPI problems?

It is often said that NP-intermediate problems, such as factoring, graph isomorphism, discrete log, and so on are "harder" than the problems in P. Meaning that they cannot be solved in polynomial time. But does this imply that all problems in P…
Andrew Baker
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Are there any "natural problems" which are known to be NPI under weak assumptions

Are there any "natural problems" which are known to be NPI under weak assumptions. By weak assumptions I mean something like $P \neq NP$ or $NP \neq Co-NP$
blademan9999
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The most subtle NP-"intermediate" problem

What is the $NP$ problem whose status in $P$ or $NP$-complete is still unsettled, as of 2018? This question is inspired by the following two recent breakthroughs: The work of Mulzer et. al on $NP$-completeness of min-weight triangulation. Recent…
Thinh D. Nguyen
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