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P versus NP problem and Polynomial-time reduction

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between P versus NP problem and Polynomial-time reduction

P versus NP problem vs. Polynomial-time reduction

The P versus NP problem is a major unsolved problem in computer science. In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine.

Similarities between P versus NP problem and Polynomial-time reduction

P versus NP problem and Polynomial-time reduction have 17 things in common (in Unionpedia): Algorithm, Complexity class, Computational complexity theory, Decision problem, EXPTIME, Graph (discrete mathematics), Graph isomorphism problem, Karp's 21 NP-complete problems, NP (complexity), NP-completeness, NP-hardness, P (complexity), Polynomial hierarchy, PSPACE, Reduction (complexity), Stephen Cook, Time complexity.

Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Complexity class

In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.

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Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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Decision problem

In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.

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EXPTIME

In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that have exponential runtime, i.e., that are solvable by a deterministic Turing machine in O(2p(n)) time, where p(n) is a polynomial function of n. In terms of DTIME, We know and also, by the time hierarchy theorem and the space hierarchy theorem, that so at least one of the first three inclusions and at least one of the last three inclusions must be proper, but it is not known which ones are.

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Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

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Graph isomorphism problem

The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.

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Karp's 21 NP-complete problems

In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.

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NP (complexity)

In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.

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NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

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NP-hardness

NP-hardness (''n''on-deterministic ''p''olynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP".

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P (complexity)

In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.

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Polynomial hierarchy

In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes P, NP and co-NP to oracle machines.

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PSPACE

In computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomial amount of space.

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Reduction (complexity)

In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem.

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Stephen Cook

Stephen Arthur Cook, (born December 14, 1939) is an American-Canadian computer scientist and mathematician who has made major contributions to the fields of complexity theory and proof complexity.

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Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

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The list above answers the following questions

P versus NP problem and Polynomial-time reduction Comparison

P versus NP problem has 146 relations, while Polynomial-time reduction has 34. As they have in common 17, the Jaccard index is 9.44% = 17 / (146 + 34).

References

This article shows the relationship between P versus NP problem and Polynomial-time reduction. To access each article from which the information was extracted, please visit:

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