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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 NP and co-NP. Each class in the hierarchy is contained within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing machines. It is a resource-bounded…

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Overview

Definitions

Relations between classes in the polynomial hierarchy

Relationships to other classes

Problems

General references

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Map overview Semantic statistics

Polynomial hierarchy

Nodes53
Edges52
Triples81
Avg. degree1.96
Density0.037736
Components1

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Polynomial hierarchy

Top relations

related to General references · 43
Polynomial hierarchy → Addison-Wesley, Arora, Automata Theory, Barak, Boaz, Cambridge University Press, Chapter, Complexity Theory, Computational Complexity, Computers, David, Freeman, Garey, Guide, IEEE Symposium, In Proceedings, Intractability, ISBN, Johnson, Lock-gray-alt-2
related to Problems · 22
Polynomial hierarchy → An, Boolean, CM, Compendium, Each, Garey/Johnson-style, In, Let, Pi, PSPACE-complete, QBFk, QSATk, Sigma, That, The, This, TQBF, We, X1, X2
related to Relationships to other classes · 5
Polynomial hierarchy → It, One, PH, PSPACE, The
related to Quantified Boolean formulae definition · 4
Polynomial hierarchy → For, In, Similarly, The
is a · 2
Polynomial hierarchy → analogue, complexity class PH.The definitions imply the relations
related to Oracle definition · 2
Polynomial hierarchy → For, Then
related to Relations between classes in the polynomial hierarchy · 2
Polynomial hierarchy → PH, The
related to Definitions · 1
Polynomial hierarchy → There

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Important terminology

hierarchy polynomial displaystyle mathrm np classes sigma problems problem class complete ph language exists turing oracle time boolean pi pspace

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Polynomial hierarchyis acomplexity class PH.The definitions imply the relations0.90text
Polynomial hierarchyis aanalogue0.90text
Polynomial hierarchyrelated to DefinitionsThere0.60section
Polynomial hierarchyrelated to General referencesLock-green0.60section
Polynomial hierarchyrelated to General referencesLock-gray-alt-20.60section
Polynomial hierarchyrelated to General referencesLock-red-alt-20.60section
Polynomial hierarchyrelated to General referencesWikisource-logo0.60section
Polynomial hierarchyrelated to General referencesArora0.60section
Polynomial hierarchyrelated to General referencesSanjeev0.60section
Polynomial hierarchyrelated to General referencesBarak0.60section
Polynomial hierarchyrelated to General referencesBoaz0.60section
Polynomial hierarchyrelated to General referencesComplexity Theory0.60section

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