Polynomial-time membership comparable sets

Mitsunori Ogihara

Polynomial-time membership comparable sets

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper introduces and studies a notion called polynomial-time membership comparable sets, which is a generalization of P-selective sets. For a function g, a set A is called polynomial-time g-membership comparable if there is a polynomial-time computable function f such that for any x₁,···,x_m with m≥g(max{|x₁|, ···,|x_m|}), outputs bqq{0,1}^m such that (A(x₁),···, A(x_m))≠b. It is shown for each C chosen from {PSPACE,UP,FewP,NP,C₌PP,MOD₂P,MOD₃P,· ··}, that if all of C are polynomial-time c(log n)-membership comparable for some fixed constant c<1, then C = P. As a corollary, it is shown that if there is some constant c<1 such that all of C are polynomial-time n^c-truth-table reducible to some P-selective sets, then C = P, which resolves a question that has been left open for a long time.

Original language	English (US)
Title of host publication	Proceedings of the IEEE Annual Structure in Complexity Theory Conference
Editors	Anon
Publisher	Publ by IEEE
Pages	2-11
Number of pages	10
ISBN (Print)	0818656727
State	Published - Dec 1 1994
Externally published	Yes
Event	Proceedings of the 9th Annual Structure in Complexity Theory Conference - Amsterdam, Neth Duration: Jun 28 1994 → Jul 1 1994

Publication series

Name	Proceedings of the IEEE Annual Structure in Complexity Theory Conference
ISSN (Print)	1063-6870

Other

Other	Proceedings of the 9th Annual Structure in Complexity Theory Conference
City	Amsterdam, Neth
Period	6/28/94 → 7/1/94

ASJC Scopus subject areas

Engineering(all)

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Cite this

Ogihara, M. (1994). Polynomial-time membership comparable sets. In Anon (Ed.), Proceedings of the IEEE Annual Structure in Complexity Theory Conference (pp. 2-11). (Proceedings of the IEEE Annual Structure in Complexity Theory Conference). Publ by IEEE.

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title = "Polynomial-time membership comparable sets",

abstract = "This paper introduces and studies a notion called polynomial-time membership comparable sets, which is a generalization of P-selective sets. For a function g, a set A is called polynomial-time g-membership comparable if there is a polynomial-time computable function f such that for any x1,···,xm with m≥g(max{|x1|, ···,|xm|}), outputs bqq{0,1}m such that (A(x1),···, A(xm))≠b. It is shown for each C chosen from {PSPACE,UP,FewP,NP,C=PP,MOD2P,MOD3P,· ··}, that if all of C are polynomial-time c(log n)-membership comparable for some fixed constant c<1, then C = P. As a corollary, it is shown that if there is some constant c<1 such that all of C are polynomial-time nc-truth-table reducible to some P-selective sets, then C = P, which resolves a question that has been left open for a long time.",

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N2 - This paper introduces and studies a notion called polynomial-time membership comparable sets, which is a generalization of P-selective sets. For a function g, a set A is called polynomial-time g-membership comparable if there is a polynomial-time computable function f such that for any x1,···,xm with m≥g(max{|x1|, ···,|xm|}), outputs bqq{0,1}m such that (A(x1),···, A(xm))≠b. It is shown for each C chosen from {PSPACE,UP,FewP,NP,C=PP,MOD2P,MOD3P,· ··}, that if all of C are polynomial-time c(log n)-membership comparable for some fixed constant c<1, then C = P. As a corollary, it is shown that if there is some constant c<1 such that all of C are polynomial-time nc-truth-table reducible to some P-selective sets, then C = P, which resolves a question that has been left open for a long time.

AB - This paper introduces and studies a notion called polynomial-time membership comparable sets, which is a generalization of P-selective sets. For a function g, a set A is called polynomial-time g-membership comparable if there is a polynomial-time computable function f such that for any x1,···,xm with m≥g(max{|x1|, ···,|xm|}), outputs bqq{0,1}m such that (A(x1),···, A(xm))≠b. It is shown for each C chosen from {PSPACE,UP,FewP,NP,C=PP,MOD2P,MOD3P,· ··}, that if all of C are polynomial-time c(log n)-membership comparable for some fixed constant c<1, then C = P. As a corollary, it is shown that if there is some constant c<1 such that all of C are polynomial-time nc-truth-table reducible to some P-selective sets, then C = P, which resolves a question that has been left open for a long time.

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