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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How can we prove that a reduction exists?

Problem: I have two computational problems, $A$ and $B$. We know that $A \in \texttt{Psearch}$ and I want to prove that $A \leq_p B$ for all problems $B$. Goal: It is my understanding that my goal is ...
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chromatic number is np-hard

I'm referring to a question in this book: Algorithms by Jeff Erickson, link:http://jeffe.cs.illinois.edu/teaching/algorithms/notes/J-approx.pdf, in particular, pg.21, Q11. The author mentioned that ...
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Relationship between complexity classes W[1]-hard and NP-hard?

If i have a parameterized reduction from multicolored independent set (W[$1$]-hard) to some problem $A$, which take polynomial time. Can i say that problem $A$ is NP-hard? in other words, Is ...
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Strategy to reduce between decision problems

I'm very new to complexity theory, please help me fill in the gaps in whatever knowledge I have acquired till now. A decision problem is a problem $X(D)$ that outputs for each input instance $I$, a ...
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Reduction techniques in complexity

I am learning computational complexity and parameter complexity. In order to proof that a problem is np-hard, we should reduction one which is np-hard to the problem. However, I don't have any idea ...
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Problem reduction: Can YES-Instances also be mapped to NO-Instances if there is perfect correspondence?

Definition: Problem A is reducible to problem B if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, ...
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Simple example of LogSpace reduction

In general, how can I verify that my many-one reduction is a LogSpace reduction? E.g. I was looking at the proof of HORN-SAT is P-complete via logspace reduction. It would be ok even if someone makes ...
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Why can't I use a polynomial-time reduction for proving P-completeness?

According to the Wikipedia page on P-complete, a decision problem is P-complete (complete for the complexity class P) if it is in P and every problem in P can be reduced to it by an appropriate ...
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Algorithm to reduce a Circuit-SAT to NAND-SAT

I am trying to construct an algorithm to reduce OR, AND and NOT gates into NAND-SAT. Can someone give me a hint as to where to start?
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If two languages are polytime reducable, does that imply they are also turing reducable

Is it possible for a pair of languages where A ≤T B but not A ≤p B? I am not sure if this could be the case since a turning reduction would imply we can use a decider for one language to decide ...
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Reduction: Does polytime reduction imply Turing reduction?

I am unsure if given $A \leqslant_p B$, does that imply that $A \leqslant_T B$. If we can polytime reduce $A$ to $B$, that would imply there is a decider for $A$ that runs in polynomial time which can ...
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Polytime Mapping Reduction from Language A to Language A (identity)

How would I create a polytime mapping reduction to prove A ≤p A for any language A. I was thinking to assume A is in P to start. For every 𝑥: 𝑥∈𝐴 iff 𝑓(𝑥)∈𝐴. But I am not sure what to do from ...
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Is there a reduction from 2sat to bpm?

Given a 2SAT instance can we convert into bipartite perfect matching in parsimonious reduction?
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Intuitive reason why the language of halting machines is Turing reducible but not many-one reducible to its complement

I have seen this statement in my studies and I cannot figure out why it is true. We know that $P_{HALT} \leq_T \overline{P_{HALT}}$, but $P_{HALT} \leq_m \overline{P_{HALT}}$ does not hold. I know, ...
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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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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 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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