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- Parity_P abstract "In computational complexity theory, the complexity class ⊕P (pronounced "parity P") is the class of decision problems solvable by a nondeterministic Turing machine in polynomial time, where the acceptance condition is that the number of accepting computation paths is odd. An example of a ⊕P problem is "does a given graph have an odd number of perfect matchings?" The class was defined by Papadimitriou and Zachos in 1983.⊕P is a counting class, and can be seen as finding the least significant bit of the answer to the corresponding #P problem. The problem of finding the most significant bit is in PP. PP is believed to be a considerably harder class than ⊕P; for example, there is a relativized universe (see oracle machine) where P = ⊕P ≠ NP = PP = EXPTIME, as shown by Beigel, Buhrman, and Fortnow in 1998. Furthermore, PPP contains PH, whereas P⊕P is not known to even contain NP.⊕P contains the graph isomorphism problem, and in fact this problem is low for ⊕P. It also trivially contains UP, since all problems in UP have either zero or one accepting paths. More generally, ⊕P is low for itself, meaning that such a machine gains no power from being able to solve any ⊕P problem instantly.The ⊕ symbol in the name of the class may be a reference to use of the symbol ⊕ in Boolean algebra to refer the exclusive disjunction operator. This makes sense because if we consider "accepts" to be 1 and "not accepts" to be 0, the result of the machine is the exclusive disjunction of the results of each computation path.".
- Parity_P wikiPageID "2120422".
- Parity_P wikiPageLength "2805".
- Parity_P wikiPageOutDegree "18".
- Parity_P wikiPageRevisionID "623963131".
- Parity_P wikiPageWikiLink Boolean_algebra.
- Parity_P wikiPageWikiLink Boolean_algebra_(logic).
- Parity_P wikiPageWikiLink Category:Complexity_classes.
- Parity_P wikiPageWikiLink Complexity_class.
- Parity_P wikiPageWikiLink Computational_complexity_theory.
- Parity_P wikiPageWikiLink Decision_problem.
- Parity_P wikiPageWikiLink EXPTIME.
- Parity_P wikiPageWikiLink Exclusive_disjunction.
- Parity_P wikiPageWikiLink Exclusive_or.
- Parity_P wikiPageWikiLink Graph_isomorphism_problem.
- Parity_P wikiPageWikiLink Low_(complexity).
- Parity_P wikiPageWikiLink Matching_(graph_theory).
- Parity_P wikiPageWikiLink NP_(complexity).
- Parity_P wikiPageWikiLink Non-deterministic_Turing_machine.
- Parity_P wikiPageWikiLink Nondeterministic_Turing_machine.
- Parity_P wikiPageWikiLink Oracle_machine.
- Parity_P wikiPageWikiLink PH_(complexity).
- Parity_P wikiPageWikiLink PP_(complexity).
- Parity_P wikiPageWikiLink Perfect_matching.
- Parity_P wikiPageWikiLink Sharp-P.
- Parity_P wikiPageWikiLink UP_(complexity).
- Parity_P wikiPageWikiLinkText "⊕P".
- Parity_P wikiPageWikiLinkText "Parity P".
- Parity_P hasPhotoCollection Parity_P.
- Parity_P wikiPageUsesTemplate Template:ComplexityClasses.
- Parity_P wikiPageUsesTemplate Template:Reflist.
- Parity_P subject Category:Complexity_classes.
- Parity_P hypernym Problems.
- Parity_P type Disease.
- Parity_P type Class.
- Parity_P comment "In computational complexity theory, the complexity class ⊕P (pronounced "parity P") is the class of decision problems solvable by a nondeterministic Turing machine in polynomial time, where the acceptance condition is that the number of accepting computation paths is odd.".
- Parity_P label "Parity P".
- Parity_P sameAs m.06nkb1.
- Parity_P sameAs Q7137529.
- Parity_P sameAs Q7137529.
- Parity_P wasDerivedFrom Parity_P?oldid=623963131.
- Parity_P isPrimaryTopicOf Parity_P.