# Questions tagged [np]

Questions about decision problems that can be solved on nondeterministic Turing machines in time polynomial in the length of the input.

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### Are there subexponential-time algorithms for NP-complete problems?

Are there NP-complete problems which have proven subexponential-time algorithms? I am asking for the general case inputs, I am not talking about tractable special cases here. By sub-exponential, I ...
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### Is there a task that is solvable in polynomial time but not verifiable in polynomial time?

A colleague of mine and I have just hit some notes of one of our professors. The notes state that there are tasks that are possible to solve in polynomial time (are in the class of PF) but that are ...
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### Is $NP$ “minimal”, i.e. does $\Pi\notin NP$ imply $\Pi$ is $NP$-hard?

Suppose $\Pi$ is a decidable decision problem. Does $\Pi\not \in NP$ imply $\Pi$ is $NP$-Hard? Edit: if we assume there exists $\Pi\in coNP\setminus NP$ then we are done. Can we refute the claim ...
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### How do we know any problem is in NP-complete if we don't know all problems in NP?

A problem is NP-complete if: It is in NP. All problems in NP can reduce to it. It's number 2 that I'm concerned with here. I would be highly surprised if we knew every problem in NP. Based on that ...
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### Is this possible when it comes to the relations of P, NP, NP-Hard and NP-Complete?

I saw an image that describes the relations of P, NP, NP-Hard and NP-Complete which look like this : https://en.wikipedia.org/wiki/NP-hardness#/media/File:P_np_np-complete_np-hard.svg I wonder if ...
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### A “natural” decidable problem not in $\mathsf{NP}$? [duplicate]

Are there any "natural" examples of decidable problems that are definitively known not to be in NP? The decidable languages I know of that are not contained in NP are usually derived from the time ...
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### How can I show that the Cook-Levin theorem does not relativize?

The following is an exercise which I am stuck at ( source: Sanjeev Arora and Boaz Barak; its not homework ) : Show that there is an oracle $A$ and a language $L \in NP^A$ such that $L$ is not ...
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### Is there any strategy to brute force search?

I don't know how to state it elegantly, but basically, I want to implement a brute force search algorithm, but there are many different ways that I could enumerate through the search space. This ...
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### Is there a more up-to-date / wider-scope version of the 'Compendium of NP Optimization Problems'

When I was studying Comp Sci, we had Garey & Johnson as a course textbook, with a large collection of NP-Complete problems. But by that time you could also have a look at the Compendium of NP ...
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### NP $\subsetneq$ EXP?

I think I heard in somewhere that it has been proven that $\mathsf{NP}$ is strictly contained in $\mathsf{EXP}$, that is $\mathsf{NP} \subsetneq \mathsf{EXP}$. Is this right? Wikipedia and book ...
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### Can proofs-of-work be probabilistically checkable?

I have been lurking for a while; this is my first post here. Iām sorry if my question is ill-formed or formatted poorly. This question came out of some ideas in another question from a sister site. ...
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### Is the closure of P under e-free homomorphisms equal to NP?

The context free languages can be obtained as the closure of the Dyck language under the cone operations. The Dyck language $D_2$ is a deterministic context free language, and the cone operations ...
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### Polytime algorithm for SUBSET-SUM assuming P=NP

In the Wikipedia page on P vs. NP problem there is an algorithm that "solves" SUBSET-SUM in case P=NP in polynomial time. (It's idea is to find a TM that gives a certificate). But it gives "yes" in ...
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### Give one example where it takes Non- deterministically exponential time to solve the problem?

I am a starter in complexity theory though I have fair knowledge in Turing machine. I know what it means to be non-deterministically polynomial time solvable but I am trying to understand where the ...
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### Does every problem in NP have an exponential time algorithm?

I am not sure that every problem in NP have an exponential time algorithm. Since NP does not mean "not polynomial.", I think the answer is false. But I have no concrete reason about that.
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### Why doesn't a time cutoff convert NP problems into co-NP? [duplicate]

Suppose you have an NP problem, and a polynomial time verifier which accepts valid solutions within $f(n)$ operations. You make a tweak to the verifier program, so that if it takes more than $f(n)$ ...
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### Why can't we exploite finiteness to prove incompleteness in NP?

It is well established that the class of recursive languages is strictly contained in the class of recursively enumerable languages (Rec $\ne$ RE). Any finite language is decidable and hence can not ...
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### Sequence to explore the complexity of the NP problem

Let $X$ be some problem known to be in $NP$. What is the natural next step in exploring the complexity of the problem? Is it trying to prove whether it is in $P$ or try to prove it is $NP$-Hard? ...
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### Are there any known lower-bounds for complexity on Non-determinsitic machines

For some problems, like sorting, we know that on a deterministic RAM Machine, any comparison sort must take at least $\Omega(n\log n)$ time. Are they any problems where we have known lower bounds for ...
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### How do we know for sure that EXPTIME ā  P?

I'm a beginner in learning about computational complexity and this has stumped me. I've read that by the time hierarchy theorem, it's known that EXP-complete problems are not in P. (Wikipedia) It ...