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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reduction from 3SUM to 3ARR-ARITH

The 3SUM problem is defined as follows. Given an array A[1...n] of numbers, determine whether there exist $i,j,k\in \{1,\cdots, n\}$ so that $A[i] + A[j]+A[k] = 0$. The 3ARR-ARITH problem is defined ...
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Reducing a CNF formula to a DNF formula in less than exponential time

The easy way is by looking at the $\{0,1\}$-table and construct the corresponding DNF formula from that, but this will take $2^n$ time. I want to do it much more efficiently. My idea is based upon the ...
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Attempt to reduce to problem of inner product

The problem of Orthogonality: gives $n$ vectors of dimension $k$ and another set of same, can a pair be found with inner product = $0$? The problem of max product: likewise two sets each $n$ vectors (...
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Reduction from SAT to EXACTSAT

PROBLEM: EXACTSAT INPUT: A boolean formula $\phi$ in CNF with $n$ variables, and a natural number $k \le n$. OUTPUT: "Yes" if and only if there is truth assignment $\theta$ which sets ...
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In-place Acceptance Problem

In-place Acceptance Problem (InAP) Instance: A deterministic Turing Machine M and a w input for it. Question: Does M accept the input w without going through cell (|w|+1)? Show that InAP is PSPACE-...
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Can I reduce from the recognition version of one probem to another without knowing the exact parameter?

I was reading the paper "Kou, L. T., Stockmeyer, L. J., & Wong, C. K. (1978). Covering edges by cliques with regard to keyword conflicts and intersection graphs. Communications of the ACM, 21(...
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Help in proving L-Completeness

I'm trying to prove that the following language is L-complete A is a language where each word is comprised of 0s and 1s & the number of 0's is double that of the number of 1's So far I've managed ...
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How to reduce SUBSET-SUM with integers to SUBSET-SUM with non-negative integers?

The subset sum problem is as follows: Given a sequence of integers $\mathcal S=(a_1, ..., a_n)$ with cardinality $n$ and an integer $T$, determine whether there is a subsequence of $\mathcal S$ whose ...
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Non-trivial reduction form SAT to $3$-SAT

Looking for any idea for reduction from $SAT \leq 3-SAT$ where $SAT$ is known to have $d$ variables at most in each clause. I am looking for a reduction in which the resulting formula will not depend ...
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Question on worst-to-average-case reductions

Consider two decision problems A and B. We know that A reduces to B in polynomial time --- if we could solve B, we have a procedure to solve A. Now, let's say it is known that the worst case instances ...
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Convert float array to lower or higher integer, find sum(integers) == round(sum(floats)), reducible to subset sum?

You have an array of floats, for example: ...
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If problem A reduces to an NP-Complete problem B, can we say that A is in NP?

I was reviewing All NP problems reduce to NP-complete problems: so how can NP problems not be NP-complete? I understand that the general way we show a problem A is in NP is to show there exists a poly-...
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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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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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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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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 ...
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 \...