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4
votes
0answers
23 views

Is there a complexity viewpoint of Galois' theorem?

Galois's theorem effectively says that one cannot express the roots of a polynomial of degree >= 5 using rational functions of coefficients and radicals - can't this be read to be saying that given a ...
-1
votes
0answers
22 views

Why is the heuristic funktion h+ a NP problem [closed]

Two questions: Why is the heuristic function h+ a NP problem, the graph does not even has cycles. Why is even planning NP-complete? There is so many graph algorithm that can be used to solve a ...
1
vote
1answer
45 views

NP HARD Problem Longest Path in Graph

I got stuck with this problem since the whole day. When we are finding the longest path in a graph we first do topological sorting and then check the path of adjacent vertices and keep upgrading ...
4
votes
1answer
234 views

Does NP-completeness require to find the solution?

In the paper "Computing Equilibria:A Computational Complexity Perspective" by Tim Roughgarden, they consider the problem: Problem 2.1 (Clique). Given a graph $G = (V, E)$ and an integer $k$: if ...
4
votes
1answer
41 views

What is an $NP^{NP}$-complete problem? [duplicate]

So in this paper I'm reading (https://adamsmith.as/papers/fdg2013_shortcuts.pdf), the authors talk about an $NP^{NP}$-complete problem, in relation to Answer Set Programming. I know what P, NP, etc. ...
1
vote
1answer
40 views

How can TSP be an NP-optimization problem, when a feasible solution $s$ must be polynomial bounded in the instance size $|I|$?

How can TSP be an NP-optimization problem ? The definition of an NP-optimization problem $\Pi$ states that for each instance $I \in \Pi$ , the set of feasible solutions $S_\Pi(I)$ is non-empty and ...
17
votes
3answers
1k views

Why are NP-complete problems so different in terms of their approximation?

I'd like to begin the question by saying I'm a programmer, and I don't have a lot of background in complexity theory. One thing that I've noticed is that while many problems are NP-complete, when ...
3
votes
1answer
28 views

Pseudo polynominal time algorithm for Np-Complete Problems

For problems like knapsack there is pseudopolynominaltime algorithm and it is np-complete. So we reduce every other problem in np in polytime to knapsack. But why don't we have then a ...
0
votes
0answers
14 views

Subexponential algorithm for Np-complete problems [duplicate]

http://cstheory.stackexchange.com/a/3627/32204 Could someone explain to me why this reasoning is false. I don't understand it! To me this sounds plausible!
1
vote
0answers
35 views

Are there any known “hard” instances for NP-Complete Problems [closed]

Are there any known "hard" instances for NP-Complete Problems, or are there no general hard instances. So for different algorithms different instances are hard?
7
votes
1answer
102 views

What do we know about NP ∩ co-NP and its relation to NPI?

A TA dropped by today to inquire some things about NP and co-NP. We arrived at a point where I was stumped, too: what does a Venn diagram of P, NPI, NP, and co-NP look like assuming P ≠ NP (the other ...
6
votes
1answer
30 views

Versions of NP with different logical unifiers

One formulation of NP is this: a language is in NP if it can be solved in polynomial time by an algorithm that has access to a special "Nondeterministic Bit" function, which branches the world into ...
0
votes
1answer
66 views

Is this problem P or NP?

Given a set of whole numbers $M=\{z_0, ..., z_n\}$ Are there $z_i$ and $z_j$ with $i \neq j$ but $z_i = z_j$? Is this Problem (surely or only probably) in $P$ or in $NP$? Is it $NP-hard$?
1
vote
1answer
36 views

IS and matching

I have 2 different but similar problems, one belongs to NP and one to L and I don't understand why. First problem: Input: an undirected graph G with n^2 vertices. Question: Is there exist in G a ...
2
votes
0answers
30 views

reduction of maxcut problem

Show that if the MAX CUT decision problem can be solved in polynomial time so can the MAX CUT optimization problem by writing an algorithm that solves the optimization problem using an algorithm for ...
-2
votes
1answer
49 views

Proof problem is NP [closed]

Hi need help to proof: For each A,B problems , if A ≤p B , and B ∈ NP then A ∈ NP Thanks.
1
vote
1answer
29 views

Reductions where the number of certificates from one problem can be computed for another to varying degrees

Let $A$ and $B$ be two decision problems in $NP$. Consider three cases: (1) For any instance of problem $A$, one can produce, in polynomial time, an instance of problem $B$ having exactly the same ...
1
vote
0answers
46 views

Subset-Sum Problem Variant with Changing Target Sum - NP Complete? [closed]

Is the Subset-Sum Problem (SSP) with a changing target sum (which is dependent on the chosen subset) also NP-complete? If so, how would I reduce SSP to this or prove that it is NP-complete in another ...
6
votes
2answers
88 views

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 ...
-1
votes
1answer
38 views

Proving that the set of non-universal CFGs is not in NP

How do I prove that $\overline{\mathrm{ALL_{CFG}}}$ does not fall in NP, where $\qquad\mathrm{ALL_{CFG}} = \{\langle G \rangle \mid G \text{ is a CFG}, L(G) = \Sigma^* \}$
0
votes
1answer
58 views

Problem A is polynomially reducible to problem B…what can we say about A and B?

This is a question on a practice final. Problem A is polynomially reducible to problem B. Which of the following statements is correct? I. If problem A is solvable in a polynomial time then problem ...
1
vote
0answers
26 views

Algorithms for verifying and solving three-coloring [duplicate]

I found the following problem that I am trying to answer: Consider the three color problem where V, vertex set of a bipartite graph. can be partitioned into three subsets such that there is no ...
3
votes
1answer
31 views

What does the 2 in a 2-approximation algorithm mean?

Does the 2 in a 2-approximation algorithm mean the solution is within 2*OPT or OPT/2?
2
votes
1answer
30 views

What is the implication of the sentence: “if any NP complete problem is p time solvable, then all problems in NP are p time solvable”

I find this quote here on page 13 Does it mean that out of all different problems that are NP complete, if any problem is found to have a p time solution, then all the NP complete problems are p ...
4
votes
1answer
84 views

Why is Steiner Tree trivially in NP?

I'm learning about NP-completeness, and many reduction proofs start off by stating that a problem is triviallyin NP. But I can't seem to wrap my head around this. Why is this so?
3
votes
2answers
238 views

Decision problem which belongs to P reduced to a decision problem which belongs to NP?

Is it possible to have a decision problem $A$ which belongs to P and reduce it to a decision problem $B$ which belongs to NP, i.e. $A \leq_{\mathrm{p}} B$, where $A$ belongs to P, $B$ belongs to NP?
-2
votes
3answers
200 views

Is every problem in NP solvable?

Is every $\sf NP$-problem solvable or are there problems that have no working algorithm to solve but have algorithms to verify?
0
votes
1answer
82 views

Some questions about NP / coNP / CSP

I need help with the following mock exam questions. True or false? 1.) If a non-trivial $(\neq \emptyset, \Sigma^*)$ finite set is NP-complete, then $P = NP$. True. Every finite set is in $P$ and ...
1
vote
1answer
166 views

Concatenation of languages in NP

I have a hard time to understand why the concatenation of two languages over an alphabet (concatenation is in NP), doesn't imply that each of the languages for themselves are in NP. I talked with my ...
0
votes
1answer
73 views

If P = NP, then is NP = FNP?

I read FP = FNP iff P = NP which makes sense. But if P = NP, does it mean FNP = NP? Intuitively, I think no because P = NP would mean that decision problems in NP would become decision ...
2
votes
1answer
32 views

Property of two ANEAs is in NP

I have two arbitrary acyclic nondeterministic finite automata $\mathcal{A_1}$ and $\mathcal{A_2}$ and want to show that the problem $L(\mathcal{A_1}) \not \subseteq L(\mathcal{A_2})$ is in NP by ...
5
votes
1answer
58 views

Are the complements of $NP$-languages with only $n$ words of length $n$ also in $NP$?

Assuming $\Sigma = \{ 0, 1\}$.. Given a language $L$, such that for each $n\in \mathbb{N}$ we have $n$ words of length $n$ in $L$ and assuming $L\in NP$, can we prove also that $L\in Co-NP$? So it ...
4
votes
2answers
95 views

Why is the O(nW) algorithm for the Knapsack problem not a polynomial one?

On the wikipedia page for the knapsack problem it says that the runtime is $\mathcal{O} (nW)$ and goes on to say that this doesn't violate its classification as NP because the input size is related to ...
0
votes
0answers
62 views

Homomorphism erasing information

I would be grateful if anyone could help me with the tricky exerciese *7.52 from Sipser's Introduction to the Theory of Computation 3rd ed. I got stuck in proving that, if P is closed under ...
5
votes
1answer
173 views

Why does the solution of an NP problem have to be polynomial size?

I've read in "Introduction to Algorithms" (CLRS) that formal language $L$ is NP-language if and only if there is a polynomial verification algorithm $A(x, y)$ and a constant $c$ such that ...
1
vote
2answers
82 views

NP-hardness of an optimization problem with real value

I have an optimization problem, whose answer is a real value, not an integer such as vertex cover and set cover. Therefore, the decision version of my problem is given an input and a real value $r$. ...
0
votes
2answers
88 views

Execution time of NP and NP-Complete algorithms

For P algorithms, we say that the execution time can be logarithmic O(log n), lineal O(n), quadratic O(n^2), etc. For NP and NP-Complete algorithms is there a way to represent the execution time? Or ...
1
vote
1answer
99 views

Reduction to Maximum Independent Set

Suppose you had a set $P$ of people. Every person $p_j \in P$ is familiar with atleast one other person $p_i$ (familiarity is symmetric). Is there a subset $S$ of people such that for $|S| \ge k$, no ...
1
vote
1answer
83 views

if $L\in NP\cap Co-NP$ is NP-Hard, then $NP=Co-NP$

I'm looking for a proof to the claim stated in the title: if $L\in NP\cap Co-NP$ is $NP$-Hard, then $NP=Co-NP$. I read the proof from my professor's recitation, but couldn't understand it, and I was ...
20
votes
3answers
292 views

NP-complete problems not “obviously” in NP

It occurred to many that in all the $\textbf{NP}$-completeness proofs I've read (that I can remember), it's always trivial to show that a problem is in $\textbf{NP}$, and showing that it is ...
-1
votes
1answer
45 views

Is P^SAT subset of sum of NP and co-NP

I have a following problem: Let $P^{SAT}$ be a class of problems decidable by a deterministic polynomial Turing Machines with SAT oracle. (only one question to oracle). Assume that: $co-NP \neq NP ...
1
vote
2answers
89 views

Do all decidable problems lie in the class NP?

All decision problems (i.e.language membership problems), which are verifiable in polynomial time by a deterministic Turing machine are called NP problems. Further, these problems can be solved by a ...
4
votes
2answers
167 views

Is the complexity class NP computably enumerable?

The definition of the complexity class $\mathsf{NP}$ seems to ensure (as good as possible) that it is computably enumerable. It looks as if the class could be enumerated by enumerating all Turing ...
1
vote
3answers
1k views

Is the class NP closed under complement?

Is the class $\sf NP$ closed under complement or is it unknown? I have looked online, but I couldn't find anything.
3
votes
1answer
37 views

Minimum weighted arithmetic mean partion?

Assume I have some positive numbers $a_1,\ldots,a_n$ and a number $k \in \mathbb{N}$. I want to partition these numbers into exactly $k$ sets $A_1,\ldots,A_k$ such that the weighted arithmetic mean ...
7
votes
1answer
479 views

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 ...
7
votes
1answer
142 views

NP Problems with unique solution

Is there any class of NP problems that have one unique solution? I'm asking that, because when I was studying cryptography I read about the knapsack and I found very interesting the idea.
4
votes
1answer
65 views

$NP\subseteq TIME[O(n^{\log n})]$

Is it more plausible that $NP\subseteq TIME[O(n^{\log n})]$ than $NP\subseteq P$? I don't see this mentioned much and is there a reason why? If this question doesn't make sense, explain why.
0
votes
1answer
86 views

NP Problem definition – verifiable on DFA vs. solvable on NFA

So in complexity theory, I've run across different definitions for NP problems -- Decision problems where a solution can be verified by a DFA in polynomial time Decision problems where a solution ...
2
votes
3answers
151 views

Why is SAT in NP?

I know that CNF SAT is in NP (and also NP-complete), because SAT is in NP and NP-complete. But what I don't understand is why? Is there anyone that can explain this?