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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What wold a NP reduction look like?

From my theory of computation lecture I recall: If $A \le_m B$ and $B$ is decidable then $A$ is decidable (uses a computable function as a reduction). If $A \le_p B$ and $B$ is in $P$ then $A$ is in ...
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Reduction from Edge-Coloring and Vertex-Coloring to a new problem

I have a question from a test I did and failed, a question I failed to do. In short: the question is about reduction from Vertex-coloring and Edge-coloring, to a new problem they have defined. The new ...
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58 views

Reduction from problem A to another problem B

I have a question from a test that I failed to pass, I failed to do the question. The question: Let A and B have two languages so that there is a reduction function f: $A\leq _pB$. Suppose that $A \in ...
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Reduction between CLIQUE to SUBSET SUM

I have a question from a test that I failed to pass, I failed to do the question. The question is about the reduction between Clique and Subset Sum. I tried to find an explanation for this on the ...
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34 views

Reduction from language in P to another language in NP

I have a question I was unable to do, from a last test I had. This is the question: Will be $A \in NP$ Let $c \in P$ be a language so that there exists $C \leq _pA$. Determine which of the following ...
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Reduction from the SAT problem to the NAE-SAT problem

I study complexity and computation independently. I have a problem that I can not solve. That's the problem: For the SAT problem, there is a version in which we receive as input phrase $\varphi$ in ...
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Reduction from the Clique problem to the Odd Clique problem

I have a question that is not clear to me, and I have not been able to answer it from a test I had. This is the question: Let's look at the problem $Oclique$ , In it we get a graph $G = (V,E)$ , And ...
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Complications of a language that reaches a state of reject

I have a question that is not clear to me, and I have not been able to answer it from a test I had. This is the question Let's look at the language $L_\mathrm{reject} = ${ $\left \langle M,w \right \...
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Reducing subsetsum to {<G, l, u> | G is a weighted graph that has a spanning tree with weight between l and u}

How can I reduce Subsetsum (or maybe other np-complete problem) problem to the problem below? input : a weighted graph $G$ and numbers $l$ and $u$. output : Does $G$ has spanning tree, $S$, such that $...
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tautology vs satisfiability

I had a test that I failed to pass, and it had a question that I failed to do. This is the question: Let us look at the language TAUTOLOGY: Collect all the phrases $\varphi$ so that each placement on ...
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1answer
64 views

Reduction from TSP to even TSP

I have a question from a test that I failed to pass, I failed to do the question. The question: Let's look at the problem of the even-length traveling agent. Given graph $G = (V,E)$ and a weight ...
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1answer
60 views

Complexity of the language that enters an infinite loop

A few days ago I had a test that I failed to pass, and it had a question that I failed to do. This is the question Let's look at the language $L_\mathrm{loop} = ${ $\left \langle M,w \right \rangle$ | ...
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Relationship between complexity classes W[1] and NP?

I am trying to understand the connection between The W-hierarchy as presented in chapter 13 of this book by Cygan et al. and the notion of the NP problems. Is the existence of an FPT algorithm for a ...
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19 views

Relationship between NP and CoNP

I have a question from a test that I could not pass, I could not answer the question and I am looking for help with this question This is the question Will be $A\in NP$ Suppose that $A\notin CoNP$. ...
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Reduction with CoNP and CoNPC

I have a question I was unable to do, from a last test I had. This is the question: Suppose that there is a language $A \neq \emptyset ,\sum{_{}}^{*}$ such that $A \in CoNP - CoNPC$. Determine ...
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Reduction between p np conp [closed]

Hello everyone I am new here on the site, I had a test a few days ago that I failed, and there was this question that I could not understand. Given: Question 1 Suppose there is a reduction . ...
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25 views

How to know if language is in comp or np?

I'm new to the site. I had a test a few days ago and failed it, I had a question I did not understand. This is the question: Let's look at the FALSE language: Collect all the verses P in the form of ...
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Given graph $G=(V,E)$ and weight function $w\,:\,E\to\mathbb{N}$, function $f(G,w)$ finds the heaviest clique in the graph, prove $L(M)=CLIQUE$

Given graph $G=(V,E)$ and weight function $w\,:\,E\to\mathbb{N}$, function $f(G,w)$ finds the heaviest clique in the graph, when the sum of a clique is the sum of the weights on all of the edges. I ...
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Why this problem is NP-Hard?

I'm asking about the question described here: Knapsack Problem with exact required item number constraint Can't we iterate over $\binom{n}{L}$ options (which is polynomial), and for each option check ...
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Is there exist FPT algorithm for a variant of VC problem?

In CLOSED VERTEX COVER, we are given a graph $G$ where each vertex $v \in V(G)$ has self-utility $u_{v} \in \mathbb{N}$ and self-pollution $p_{v} \in \mathbb{N}$, and $k, U^{\star}, P^{\star} \in \...
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How to prove Dense Subgraph problem is in NP

I have been studying NP-Complete problems and I saw the Dense Subgraph problem. Then I saw that they are trying to show that the problem is NP (see below quote), but I can't understand how it verifies ...
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NP problem: certificate concept clarification

When proving a problem in NP, e.g. k-clique problem defined as k-clique:= {<G,k>| G has a clique of size at least k }, from what I understand is that all we assume for the certificate "c&...
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How far would complexity hierarchies collapse if $L\in CoNP$ is $L\in NPH$?

Let $L\in CoNP$. Assuming that $L\in NPH$, what would we get? So, as $L\in NPH$ then every language $A\in NP$ has a reduction $A \leq L$. This would mean that $\overline{L} \leq L$ as well. By ...
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NP-complete problem

Is the following line true? Consider three problems A, B and C. If $A$ $<p$ $B$ and $B$ $<p$ $C$ and $B$ is NP-complete problem, then $C$ is also NP-complete. If B is NP-complete, then C would ...
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NP Reduction - Dominating set to SAT

Given a graph G and an integer k , recognize whether G contains dominating set X with no more than k vertices. And that is by finding a propositional formula ϕG,k that is only satisfiable if and only ...
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Does $NP^{SAT}=NP^{NP}$?

Does $NP^{SAT}=NP^{NP}$? We can see easily that $NP^{SAT}\subseteq NP^{NP}$, because $SAT \in NP$. But is the other side $NP^{NP}\subseteq NP^{SAT}$ also true? If yes, how can we prove it?
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Easy proof for $Primes \in NP$

I want to show that $Primes \in NP$ an I've seen multiple proofs that use facts from number theory, like this one. But isn't it much easier to proof $$Composites=\{x\in \mathbb{N}\cup\{0\}:x=1 \vee\...
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If $S\in\left(NP\bigcup coNP\right)$ then $\overline{S}\in NP\bigcap coNP$?

Is it true that if $S\in\left(NP\bigcup coNP\right)$ then $\overline{S}\in NP\bigcap coNP$? I couldn't find any answer to that question. My attempt at proving it: If $S\in\left(NP\bigcup coNP\right)$, ...
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polynomial reduction within Np

If $A \le_p B$ and $B\in NP$, does it necessarily follow that $A\in NP$? ($\le_p$ is a polynomial many-one reduction) A quick yes/no comment is enough, a proof would be nice :-)
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Language in $R \setminus \mathit{NP}$

I am wondering whether the language $$L_{\textrm{hanoi}} = \{\langle k,s \rangle \mid \text{$s$ is a solution of Tower of Hanoi problem on $k$ rings}\}$$ is in $R\setminus \mathit{NP}$. I want to ...
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Assume P != NP, are these assertions valid?

Assume $P \ne NP$, and $A$ is a problem in $P$ and $B$ is a problem which is $NP-complete$. Are the following assertions valid? $A \le_{P} B$ $B \le_{P} A$ My approach: $B \le_{P} A$ isn't valid, ...
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Are the following assertions true if P != NP?

We consider the NP-complete $CLIQUE$ problem. Let furthermore $MST^*$ be the minimum spanning tree problem. Assume that $P \ne NP$ and explain whether the following assertions hold: $MST^* \le_{P} ...
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Is quadratic nonresiduosity in $\textbf{NP}$?

The paper "The Knowledge Complexity of Interactive Proof Systems" uses the language of quadratic nonresidues defined via the following excerpt from page 293 as an example of constructing an ...
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How to reduce the hamiltonian path problem to 1/2 hamiltonian path problem

Task: A Hamiltonian path of a graph is a path that visits all nodes of the graph exactly once. The hamiltion path problem (HPP) consists in deciding whether a given graph has such a path. Similarly, ...
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Is every problem with an output's size that grows polynomialy np?

I am wondering if every problem with an output's size that grows polynomialy is $\textsf{NP}$? My thinking is every $\textsf{NP}$ problems can be solved in polynomial time by a non-deterministic ...
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Non-brute force algorithm for a Eulerian like path

I have a graph with an arbitrary amount of edges and vertexes. Each vertex having an arbitrary amount of edges connecting to it but in practice the number is usually around 3 or 4 no less than one ...
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Karp's reduction strategy

One way to prove that a problem $X$ is NP-Complete is to pick two NP-Complete problems $Z$ and $W$ and show that ($\leq_p$ is polynomial reduction): $$\begin{array}{rr}X \leq_p Z & (1)\\W \leq_p X&...
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Is there any NP-hard problem which was proven to be solved in polynomial time or at least close to polynomial time?

I know this could be a strange question. But was there any algorithm ever found to compute an NP-problem, whether it be hard or complete, in polynomial time. I know this dabbles into the "does P=...
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Color coding to get an FPT algoirthm for k disjoint triangles

The k-disjoint triangles problem is as follows: Input: A graph $G=(V,E)$ and an integer $k\in \mathbb{N}$ Output: Are there $k$ vertex-disjoint triangles in $G$? An FPT algorithm is presented here (...
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Proving a problem is NP Hard

Consider the following problem: Given a weighted directed graph $G$, determine if $G$ has a cycle whose total weight is $k$. All edge weights are integer but might be negative. $k$ is not an inputted ...
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IS SUBSET-SUM in P if b(the sum) is given in unary and a1,…,an is in binary?

The SUBSET SUM decision problem consists of poitive integers a1,...,an; b. We wish to know if for some subset S of the indices, $\sum_{i \in S}a_i = b$ I want to prove that if b is given in unary(...
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How can I prove the following problem is NP complete?

The problem: I have a list $\displaystyle S=\{s_{1} ,s_{2} ,\dotsc ,s_{n}\}$ places. Each unordered pair of places has cost and gain: $\displaystyle c\{s_{i} ,s_{j}\} \in \mathbb{N}$, $\displaystyle g\...
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Given N positive integers are they the integers 1-N : What is the relationship between this problem and NP?

Here’s the decision problem: Suppose I have N positive integers encoded in base-2 (as oppose to unary) Are these integers precisely the integers 1-N in some order? This is related to the Hamiltonian ...
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Are problems that are fractions of constraints of NP-complete problems also NP-complete?

We know that Hamiltonian path, clique and independent sets are NP-complete but what about half or the square root of each problem or a fraction of $n$ ? That is, for a graph, $G$ of $n$ nodes, is ...
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What is the difference between NP and co-NP? [duplicate]

I'm trying to understand the very simple concept of co-NP but I can't figure it out. On wikipedia, it gives the example of SAT and its complement: The complement of any problem in NP is a problem in ...
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If a problem A has a poly-time reduction to a problem B in co-NP, is A in co-NP as well?

i.e. $A\leq_pB\:\wedge\:B\in\text{co-NP}\rightarrow A\in\text{co-NP}$ ? I feel like it's the case but I can't think of a straightforward proof. Clarification: I am talking about polynomial-time Turing ...
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If P = NP, do these NP-complete problems reduce to these specific easier versions?

I am trying to understand reductions and NP-completeness from Algorithms by Dasgupta et al. Chapter 8 has the table below and I am wondering: if $P = NP$ does each of the problems on the left reduce ...
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Reduction from Clique to IS degree at most 4

This is from the Algorithms textbook by Dasgupta,C. H.Papadimitriou,andU. V. Vazirani question 8.6 (b) that asks: Edit: And missing from the pic as @Nathaniel points out in his answer below: "...
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How to prove NP-completeness of this mail-problem?

Let's say we have n postmen that are bringing people mail in a neighbourhood, and that they start and end at the same post office. This situation can be decribed with a directed graph, where the ...
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Showing that a problem in $NP$ admits two distinct verifiers that satisfy additional constraints

Show that any $S \in NP$ has 2 different polynomial-time verifiers $V_1, V_2$ such that, for all $x,y$, the following conditions hold: If $V_1(x,y)=1$ then $V_2(x,y)=0$ If $V_2(x,y)=1$ then $V_1(x,y)=...

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