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P versus NP problem

The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every decision problem for which a proposed positive answer can be quickly verified can also be quickly solved.

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Example

History

Context

NP-completeness

Harder problems

Problems in NP not known to be in P or NP-complete

Comparison of P with "easy" problems

Reasons to believe P ≠ NP or P = NP

Consequences of solution

Results about difficulty of proof

Logical characterizations

Polynomial-time algorithms

Formal definitions

Claimed solutions

In popular culture

Similar problems

Sources

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Map overview Semantic statistics

P versus NP problem

Nodes167
Edges166
Triples70
Avg. degree1.99
Density0.011976
Components1

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P versus NP problem

Top relations

related to Sources · 23
P versus NP problem → Archived, August, Cook, Dean, Encyclopædia Britannica, Hosch, June, Just, Levin, Mathematics Remain Mostly Mysterious, May, Millennium Prize Problems, NP, NP Problem, NP-problem, Rachel Crowell, Retrieved, Space, Suppose, The Top Unsolved Questions
related to history · 14
P versus NP problem → Although, Gödel, If, In, John, John Nash, Kurt Gödel, Leonid Levin, National Security Agency, Neumann, NP, NP-complete, Stephen Cook, The
related to Reasons to believe P ≠ NP or P = NP · 14
P versus NP problem → According, Cook, Does, Furthermore, It, Karp's, List, NP, NP-complete, NP-completeness, PH, The, These, Versus NP Problem
related to In popular culture · 10
P versus NP problem → Homer, Horror VI, In, NP, The, The Simpsons, Timothy Lanzone, Travelling Salesman, Treehouse, US
related to Claimed solutions · 5
P versus NP problem → Gerhard, NP, Some, While, Woeginger
is a · 1
P versus NP problem → major unsolved problem in theoretical computer science

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Important terminology

np problem problems polynomial time np-complete algorithm would known also complexity many answer polynomial-time proof solution one whether algorithms machine

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
P versus NP problemis amajor unsolved problem in theoretical computer science0.90text
BPPinstance ofleading to classes0.80text
BQPinstance ofleading to classes0.80text
3-SAT would break most existing cryptosystems includinginstance ofA constructive and efficient solution to an NP-complete problem0.80text
P versus NP problemrelated to Claimed solutionsWhile0.60section
P versus NP problemrelated to Claimed solutionsNP0.60section
P versus NP problemrelated to Claimed solutionsGerhard0.60section
P versus NP problemrelated to Claimed solutionsWoeginger0.60section
P versus NP problemrelated to Claimed solutionsSome0.60section
P versus NP problemrelated to historyThe0.60section
P versus NP problemrelated to historyNP0.60section
P versus NP problemrelated to historyStephen Cook0.60section

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