About: Polynomial hierarchy

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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 counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic. The union of the classes in the hierarchy is denoted PH.

Attributes	Values
rdf:type	software
rdfs:label	Polynomial hierarchy (en)
rdfs:comment	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 counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic. The union of the classes in the hierarchy is denoted PH. (en)
sameAs	Polynomial hierarchy Polynomial hierarchy
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Mvar dbt:No_footnotes dbt:Reflist dbt:Tmath dbt:Unordered_list dbt:ComplexityClasses dbt:Unsolved dbt:Mathcal
Subject	Structural complexity theory Hierarchy
gold:hypernym	Hierarchy
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Polynomial_hierarchy?oldid=1060729933&ns=0
Wikipage page ID	658651 (xsd:integer)
page length (characters) of wiki page	15718 (xsd:nonNegativeInteger)
Wikipage revision ID	1060729933 (xsd:integer)
has abstract	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 counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic. The union of the classes in the hierarchy is denoted PH. Classes within the hierarchy have complete problems (with respect to polynomial-time reductions) which ask if quantified Boolean formulae hold, for formulae with restrictions on the quantifier order. It is known that equality between classes on the same level or consecutive levels in the hierarchy would imply a "collapse" of the hierarchy to that level. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Polynomial_hierarchy
is Wikipage redirect of	Sigma2p NP^NP Polynomial-time hierarchy Polynomial time hierarchy
is Link from a Wikipage to another Wikipage of	List of terms relating to algorithms and data structures List of unsolved problems in computer science List of unsolved problems in fair division Logic optimization Mahaney's theorem NP-easy NP/poly NP-completeness AC0 Albert R. Meyer Alternating Turing machine Arithmetical hierarchy Arthur–Merlin protocol BPP (complexity) BQP Belief revision Berman–Hartmanis conjecture Boolean circuit Boolean hierarchy Boolean satisfiability problem Boson sampling Bounded arithmetic Bounded quantifier Circuits over sets of natural numbers Default logic Delta List of mathematical logic topics Closed-world assumption Complexity class Algorithmic complexity Hierarchy (mathematics) List of complexity classes List of computability and complexity topics Michael Sipser Envy-free item allocation Graph isomorphism Graph isomorphism problem Indistinguishability obfuscation Karp–Lipton theorem Descriptive Complexity Descriptive complexity theory Exponential hierarchy Hedonic game Induced matching Intersection number (graph theory) Lance Fortnow Larry Stockmeyer Limits of computation Maximin share Nerode Prize Low (complexity) NP^NP

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