Questions tagged [reductions]

In computability and complexity, finding mappings between problems that allow solving one problem using a solution of another one. For reduction in programming language theory (e.g. beta-reduction), see [lambda-calculus] or [term-rewriting].

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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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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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1answer
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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 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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1answer
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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 from IS problem to other problem [closed]

Given graph 𝐺 = (𝑉, 𝐸) it is said that it is a star if there is a vertex $𝑣_0 ∈ 𝑉$ so that all the other vertices are connected exclusively to it (and not to ...
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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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1answer
31 views

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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1answer
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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
36 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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edge-coloring and vertex-coloring reduction problem

I study complexity and computation independently. I have a problem that I can not solve. That's the problem: Edge-Coloring problem, we get as input graph G = (V, E) and natural number k and ask "...
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1answer
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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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Reduction from vertex-coloring problem to edge-coloring problem

A few days ago I had a test and could not pass it. This is a question I did not understand in the test. We will look at the Edge-Coloring problem, in which, as is well known, we get as input graph G =...
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1answer
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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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edge-coloring reduction problem

I study complexity and computation independently. I have a problem that I can not solve. That's the problem: Edge-Coloring problem, we get as input graph G = (V, E) and natural number k and ask "...
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NP-Hardness of $\{ (S,k) | \exists S' \subset S \text{ s.t } \forall x \neq y \in S' \gcd(x,y)=1 \text{ and } \sum_{s \in S'} s \geq k \}$

I have been practicing NP-Hardness reductions and have been particularly interested in the language $L = \{ (S,k) | \exists S' \subset S \text{ s.t } \forall x \neq y \in S' \gcd(x,y)=1 \text{ and } \...
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1answer
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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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Language in NPC and CoNP

A few days ago I had a test that I failed to pass, and it had a question that I failed to do. the question: given: $A \in NPC$ $A \in CoNP$ Determine which of the following statements is correct: $P\...
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1answer
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Reduction with NPH

I have a question in complexities that I could not do. There will be D, E, F, three languages belonging to NPH. Suppose that the reductions exist $D \leq _P E$ and $E \leq _P F$. Determine which of ...
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1answer
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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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Equivalence of algorithms with less than vs equal to constrains

Problem A: Given an algorithm $\mathcal{A}$ for $(I,k)$,$k\in \mathbb{N}$, $A$ return true $\iff$ There exist a subset $S\subseteq I$ s.t $|S| \le k$ some property hold. Problem B: Given an algorithm $...
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Reduction from SAT to 3SAT

a few days ago I had a test and could not pass it. This is a question I did not understand in the test. Recall the reduction we saw $SAT \leq _p 3SAT$. Given verse $\varphi$ in the form of $CNF$, we ...
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Deteremine if $L = \{\langle M\rangle : L(M) \text{ consits of all words of prime length}\}$ is in $R$ or in $RE\setminus R$ or not in $RE$

Deteremine if $L = \{\langle M\rangle : L(M) \text{ consits of all words of prime length}\}$ is in $R$ or in $RE\setminus R$ or not in $RE$ I am trying to prove that $L$ is not in $RE$ by reduction ...
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Proving that a problem is not FPT using reduction

In the Inclusive Vertex Cover problem, For a given graph $G=(V,E)$, each vertex $u\in V(G)$ has weight $u_{w} \in \mathbb{N}$ and value $u_{v}\in \mathbb{N}$. The value and weight of a set cover $S$ ...
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Understand what this phrase is in the Turing

I had a test a few days ago and failed it. There was a question that was not clear to me. This is the question: For the purpose of describing the drawing on the tape of a Turing machine at each step ...
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1answer
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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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1answer
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SUBSET SUM reduction to PARTITION

This is the PARTITION problem: Given a multiset S of positive integers, decide if it can be partitioned into two equal-sum subsets. This is the SUBSET SUM problem: Given a multiset S of integers ...
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PCP undecidability

There is a popular proof for the undecidability of the PCP (Post correspondence problem), which is outlined here: https://en.wikipedia.org/wiki/Post_correspondence_problem I'll assume whoever will ...
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Question about reduction Proof

I've recently seen a proof that the set of Turing machines $L = \{encode(M) |L(M) \text{is closed under reversal}\}$ is not decidable. The proof used following idea: Reduce from the $A_{TM}$ problem ...
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Prove that the Language $L=\{code(M)\;|\;L(M)\; \text{is closed under reversal}\}$ is undecideable

I want to solve this problem using Many-One-Reduction, which involves, if I understood it correctly, reducing another problem on the problem stated in the title, i.e. $$ H \leq_M L $$ I would try ...
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Connection between planar graph and vertex cover

I have two similar problems in which I'm trying to find a connection to help me solve one of them. In the first one I'm given a graph G = (V,E) , integer k, and vertex cover U of size k. The objective ...
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1answer
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Reduction from 2 finite languages when one doesn't include epsilon and the other does

Just did a test about the subject that had the following question: I know it seems trivial and my first reaction was "well of course its true" but the epslilon kinda threw me off. $L_2$={ab,$...
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1answer
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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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Reduction rules to lower bound minimum degree of a graph

I'm trying to come up with a list of rules that return an equivalent instance to the following problem, while eliminating all vertices of degree 2 or less from the graph: Given a graph $G=(V,E)$, the ...
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1answer
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Issues in the proof of $E_{TM}$ is Turing reducible to $A_{TM}$

First definition: $A_{TM}$ = $\{ <M,w> | $M is a TM and M on w accepts$ \}$ Second definition: $E_{TM} = \{ <M> |$ M is a TM and L(M) = $\phi \}$ Let $T^{A_{TM}}$ be an oracle Turing ...
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Show that $3SAT$ is a polynomial reduction on $MSAT$, i.e. $3SAT \leq_p MSAT$ [duplicate]

The exact definition of $3SAT$ and $MSAT$ are as follows: $3SAT :=$ each clause has exactly 3 literals $MSAT :=$ At least half of the literals of every clause are True My intuition was, as we know ...
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How to encode reachability in a graph with walls as a SAT problem

Suppose we have a graph that represents a grid of cells. We are given a cell to start in and a cell that's the destination. There are cells that we cannot enter and they are known as walls. Finally we ...
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Mistake in Karp's paper on NP-Complete problems?

I read on a blog that there are mistakes in Karp's paper where he proved that 0-1 programming is NP-Complete, but I couldn't find it, can anyone explain? And I doubt that there are also mistakes where ...
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Prove ALL$_{\text{TM}}$ is undecidable reduction problem

Given ALL$_{\text{TM}}$ = { < M > | where M is a TM and L(M) = $Σ^*$ } show this is undecidable. I'm also told not to use Rice's theorem. I'm having difficulties with reduction type problems. How ...
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Delivery problem, unsure which exact problem it is

I'm looking for guidance on how to reduce the following problem to a known problem or a suggestion for solving it altogether. Optimal / heuristic solutions or any other suggestions are greatly ...
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1answer
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How to prove that $L_{D}\leq L_{U}$?

I have the following two languages: $$ L_{U}\triangleq\left\{ \langle M,x\rangle\,:\,M\text{ accepts }x\right\} ,L_{D}\triangleq\left\{ \langle M\rangle\,:\,M\text{ accepts }\langle M\rangle\right\} $...
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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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198 views

Efficient algorithm to determine if a lambda calculus term is equivalent to one without a given free variable

Consider the following problem: given a lambda calculus term $t$ and free variable $v$ determine whether $\phi(t,v)$, where $\phi(t,v) := \exists t'. t' \equiv t \land v \notin FV(t')$. This problem ...
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1answer
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Is $L=\{\langle M\rangle\mid L(M)\subseteq HP\}\in coRE$?

My intuition is that $L\notin coRE$, but I haven't managed to prove that $HP \le L$, as previously I only saw reductions from $HP$ or from $\overline{HP}$ with $f$ such that $f((\langle M\rangle,x))=\...
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Mapping reductions for dummies

I am having trouble understanding a mapping reduction and I would appreciate your help. Define $\quad \begin{align} A_{TM} &= \{ \langle M, w \rangle \mid M \text{ Turing machine}, w \in \...
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1answer
27 views

Proving undecidability of a language with mapping reductions

I'm referring to questions like this one: Mapping reduction to show NeverHalt is undecidable I understand with Turing reductions, you have to use oracle calls of the unknown language you're trying to ...
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Is the problem “find the sequence of $N$ numbers between 1 and $D$ with least cost”, NP-hard?

Consider sequences $p=(p_1,\dots,p_N)$ (the order matters) of length $N$, where $p_i\in\{1,\dots,D\}$ for fixed $D$. Moreover, consider a cost function $c:\{1,\dots,D\}^N\to\mathbb{R}$ which comply $c(...
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Reduction from set cover problem to vertex cover problem

Although the reduction from vertex cover problem to set cover problem is quite simple, I did not find anywhere the reduction in the opposite direction. From the similarity in the type of problems, I ...
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1answer
28 views

Is this variation of the traveling salesman problem NP-hard

Consider the following setting. You have $n$ cities, and there is a cost to travel from a city $i$ to a city $j$ given by $c_{ij}>0$ where $c_{ij}\neq c_{ji}$. Moreover, if you are traveling to ...
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Is this combinatorial seach problem NP-complete?

The context: Consider the following optimization problem. Let $f_1,\dots,f_L:\mathbb{R}\to\mathbb{R}$ arbitrary (continous) functions for $L>1$ and $x_k\in\mathbb{R}$ evolve according to $$ x_{k+1}...

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