NP stands for Nondeterministic Polynomial time.

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14
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1answer
301 views

Does PSPACE-completeness imply approximation hardness?

It is mentioned in a comment in another cstheorySE post that PSPACE-completeness imply APX-hardness. Can anyone please explain/share a reference for it? Is this "tight"? (i.e., are there ...
2
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0answers
162 views

Does $P\neq NP$ imply any larger separation?

I've asked a similar question in cs.se, but didn't get a satisfying answer. Assuming $P\neq NP$, what can we say about the runtime of any algorithm for an $NP$-complete problem? Obviously, it means ...
11
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3answers
310 views

NP-complete graph property that is hereditary, but not additive?

A graph property is called hereditary if it closed with respect to deleting vertices (i.e., all induced subgraphs inherit the property). A graph property is called additive if it is closed with ...
25
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7answers
1k views

Nontrivial membership in NP

Is there an example of a language which is in $NP$, but where we cannot prove this fact directly by showing that there exists a polynomial witness for membership in this language? Instead, the fact ...
11
votes
1answer
272 views

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 ...
6
votes
1answer
102 views

Can NP-hard statements be proved by PCPs that only involve reading 2 bits?

For non-negative integers q, let PCP(q) denote the set of promise problems that have polynomial-length probabalistically checkable proofs over the binary alphabet in which the verifier only reads q ...
1
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1answer
169 views

Complexity of an edit distance problem

Given an array $A[1...n]$ of non-negative integers, we want to transform $A$ into $A'$ such that $|A[I] - A[I + 1]| \leq 1$ in the minimum number of operations. One operation consist of picking ...
-1
votes
1answer
166 views

Deciding whether a turning machine guaranteed to halt solves sat [closed]

Suppose I give as input a Turing machine M guaranteed to halt in time n^c on inputs of length n for a universal constant c. Is there a Turing machine that given any such M can decide whether M solves ...
5
votes
2answers
292 views

Public-key encryption without the assumption that $P \neq NP$

I'm not talking about the RSA, El-gamal, nor any specific encryption scheme. Rather, my question, as related to this and this threads, is why the idea of Public-Key encryption scheme cannot be secure ...
2
votes
1answer
155 views

Dividing users with certain files into 2 equal groups

I am framing a particular combinatorial question using users and files for better understanding. Let there be a universe of files $F$ = $\{f_1, f_2,\ldots,f_n\}$ and $2k$ users $\{u_1, u_2,\ldots, ...
22
votes
2answers
802 views

Reasons to believe $P \ne NP \cap coNP$ (or not)

It seems that many people believe that $P \ne NP \cap coNP$, in part because they believe that factoring is not polytime solvable. (Shiva Kintali has listed a few other candidate problems here). On ...
6
votes
1answer
181 views

Consequences and state-of-the-art of NP ≠ ZPP?

Consider the complexity classes $\mathsf{NP}$ and $\mathsf{ZPP}$. Whether the two classes are equal is an open question, but as far as I know, $\mathsf{NP} = \mathsf{ZPP}$ is not known to imply ...
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2answers
301 views

Intersection between sets

Assume that we have $p$ sets, with given sizes: $m_1,m_2,...,m_p$. The (distinct) elements in each set are taken from $N$ elements (where $m_1,m_2,...,m_p \le N$). A combination is defined as an ...
20
votes
4answers
1k views

Best known deterministic time complexity lower bound for a natural problem in NP

This answer to Major unsolved problems in theoretical computer science? question states that it is open if a particular problem in NP requires $\Omega(n^2)$ time. Looking at the comments under answer ...
32
votes
1answer
539 views

NP-Completeness of the decision problem for the generalized 15-puzzle

I am interested in the natural generalization of the famous 15-puzzle, where you have to slide blocks until you have sorted all given numbers (usally there is a gap of 1 block). Now the ...
7
votes
1answer
375 views

Does every Turing-recognizable undecidable language have a NP-complete subset?

Does every Turing-recognizable undecidable language have a NP-complete subset? The question could be seen as a stronger version of the fact that every infinite Turing-recognizable language has an ...
5
votes
1answer
489 views

Guidelines to reduce general TSP to Triangle TSP

I am looking for the method / correct way to approach to reduce the traveling salesman problem to an instance of traveling salesman problem which satisfies the triangle inequality, ie: $D(a, b) \leq ...
7
votes
1answer
117 views

Literature for restrictions that make NPC-Problems to P

The boolean satisfiability problem is in $\mathcal{NPC}$. But if you only get Horn clauses, it is in $\mathcal{P}$. I've already heard similar statements. Do you know a more general statement when ...
6
votes
0answers
118 views

The relation between NP and IP(2pfa)

As far as I know, it is not known whether $ \mathsf{NP} \subseteq \mathsf{IP(2pfa)} $, where $ \mathsf{IP(2pfa)} $ is the class of languages having interactive proof systems with some two-way ...
2
votes
1answer
497 views

Is “meeting/room planning” NP-complete?

Short summary: The problem is to assign people to meetings at different days while respecting the capacities and (inter-day) constraints of the meetings. Each person can only attend at most one ...
0
votes
1answer
330 views

$\mathsf{DTime}(O(n^k)) \subseteq \mathsf{NTime}(g)$ for some $g \in o(n^k)$?

Can this statement be confirmed or disproved: $\mathsf{DTime}(O(n^k)) \subseteq \mathsf{NTime}(g)$ for some $g \in o(n^k)$ [Question changed to use Kaveh's brilliant formulation.] Here the NDTM ...
2
votes
0answers
196 views

Help with an np-completeness proof [closed]

I know that graph contractability is NP-complete: given $G=(V_1,E_1)$ and $H=(V_2,E_2)$, can a graph isomorphic to $H$ be obtained from $G$ by a sequence of edge contractions? Consider the following ...
19
votes
1answer
387 views

What is $\mathsf{NP}$ restricted to linear size witnesses?

This is related to the question Is the Witness Size of Membership for Every NP Language Already Known? Some natural $\mathsf{NP}$(-complete) problems have linear length witnesses: a satisfying ...
2
votes
0answers
96 views

Polynomial Quantum Algorithm for Graph Isomorphism? [duplicate]

Possible Duplicate: NP-intermediate problems with efficient quantum solutions Many suspect that quantum computers will not be able to efficiently solve NP-complete problems and thus focus ...
-1
votes
2answers
555 views

What progress has been made to prove whether or not p=np? [closed]

I know that it is still one of the biggest mysteries of computer science whether non-deterministically polynomial problems can be solved in polynomial time. I am curious to know what makes this ...
15
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0answers
577 views

Complexity of a switch network problem

A switch network (the name is invented) is made with three types of nodes: one Start node one End node one or more Switch nodes The switch node has 3 exits: Left, Up, Right; has two states L and R ...
7
votes
0answers
420 views

Is this minimization problem NP-Complete?

We are given an $n \times (n + k)$ matrix $A$, with entries in GF(2), of the form $A =[I_n\ B]$, where $I_n$ is the $n \times n$ identity matrix, and $B$ has no "zero" rows or columns. The problem is ...
18
votes
2answers
804 views

Are there known NP-complete problems, neither NP-hard in the strong sense nor having pseudopolynomial algorithm?

In their paper (p. 503) Garey and Johnson remark: ... there could exist an NP-complete problem which is neither NP-complete in the strong sense nor solvable by a pseudo-polynomial time algorithm ...
9
votes
1answer
315 views

Non-Uniform vs. Uniform Adversaries

This question arose in the context of cryptography, but below I will present it in terms of complexity theory, since people here are more acquainted with the latter. This question is related to ...
19
votes
1answer
434 views

Problems in NP but not in Average-P/poly

The Karp–Lipton Theoem states that if $\mathsf{NP} \subset \mathsf{P/poly}$, then $\mathsf{PH}$ collapses to $\mathsf{\Sigma^P_2}$. Therefore, assuming separations between $\mathsf{\Sigma^P_2}$ and ...
0
votes
2answers
2k views

Relationship between context-free/decidable languages and NP [closed]

As far as I understand all languages in NP are decidable. But not all decidable Languages are in NP, because NP only contains decision problems. Are there also decision problems that are decidable ...
5
votes
1answer
517 views

Highest lower bound on NP problems (TSP)

I'll try another question that I haven't been able to find almost any kind of information about, thanks a lot for any kind of pointers or explanations. Is there a list of the proven lower bounds of ...
0
votes
1answer
280 views

What relations has different bounds for NP?

this is my first question here so I hope I've done everything correctly. I know that if someone finds a polynomial solution to any of the famous NP problems, all of them has one (polynomial ...
11
votes
2answers
1k views

Is the half-filled magic square problem NP-complete?

Here is the problem: We have a square with some numbers from 1..N in some cells. It's needed to determine if it can be completed to a magic square. Examples: ...
21
votes
2answers
1k views

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) ...
3
votes
3answers
344 views

Is Degrees Of Separation NP Complete?

I'm doing a bit of research on doing social analysis between so called "hub" people. Basically what I want to try to do is determine the shortest paths between two individuals. The problem is that ...
11
votes
1answer
556 views

NP vs co-NP and second-order logic

Assume that NP=co-NP and polynomial $p(x)$ bounds the length of the proof of unsatisfiability for a 3-CNF instance $x$. Then are there any results on what form any proof of unsatisfiability for $x$ of ...
10
votes
1answer
332 views

Conditions for tractability of 3SAT-Satisfiability

What I'm wondering specifically is if there is an interesting condition on the percentage of assignments that satisfy a 3SAT formula to guarantee that such problems are tractable. Suppose for example ...
11
votes
1answer
311 views

Is the Witness Size of Membership for Every NP Language Already Known?

The question occurred to me when I get Dana Moshkovitz answer to another topic. Let $L$ be an NP Language, and let $R_L$ be the respective NP relation. We know that there exists some polynomial $p$ ...
2
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1answer
3k views

Difference between NP-Hard and NP-Complete [closed]

Can someone please summarize the exact difference between NP-Complete and NP-Hard problems in simple language? Wiki and my standard books aren't exactly helping.
26
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3answers
1k views

A decision problem which is not known to be in PH but will be in P if P=NP

Edit: As Ravi Boppana correctly pointed out in his answer and Scott Aaronson also added another example in his answer, the answer to this question turned out to be “yes” in a way which I had not ...
16
votes
2answers
488 views

Hardness of parameterized CLIQUE?

Let $0\le p\le 1$ and consider the decision problem CLIQUE$_p$ Input: integer $s$, graph $G$ with $t$ vertices and $\lceil p\binom{t}{2} \rceil$ edges Question: does $G$ contain a clique on at ...
-3
votes
2answers
636 views

At last P != NP or not [duplicate]

Possible Duplicate: Is the recent proof that P != NP correct? some weeks ago I heard a news that some one proof that P != NP (link1 - link2) andsome days later I heard that he was wrong (I ...
9
votes
3answers
851 views

Is there a complexity theory analogue of Rice's theorem in computability theory?

Rice's theorem states that every nontrivial property of the set recognized by some Turing machine is undecidable. I am looking for complexity-theoretic Rice-type theorem that tells us which ...
1
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1answer
171 views

Sparsity of Horn satisfiability?

Is the set of satisfiable Horn formulas sparse? A sparse language contains a polynomially bounded number of srings at every length.
24
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3answers
692 views

Natural problems in $NP \cap coNP$ not in $UP \cap coUP$?

Are there any natural problems in $NP \cap coNP$ that are not (known to be/thought to be) in $UP \cap coUP$? Obviously the big one everyone knows about in $NP \cap coNP$ is the decision version of ...
9
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3answers
469 views

Two Variants of NP

Here are two variations on the definition of NP. They (almost certainly) define distinct complexity classes, but my question is: are there natural examples of problems that fit into these classes? ...
14
votes
1answer
349 views

Best known joint containments for/by NP and Parity-P?

Parity-P is the set of languages recognized by a non-deterministic Turing machine which can only distinguish between an even number or odd number of "acceptance" paths (rather than a zero or non-zero ...