Polynomial-time membership comparable sets

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Annual Structure in Complexity Theory Conference
Editors Anon
PublisherPubl by IEEE
Pages2-11
Number of pages10
ISBN (Print)0818656727
StatePublished - Dec 1 1994
Externally publishedYes
EventProceedings of the 9th Annual Structure in Complexity Theory Conference - Amsterdam, Neth
Duration: Jun 28 1994Jul 1 1994

Publication series

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

Other

OtherProceedings of the 9th Annual Structure in Complexity Theory Conference
CityAmsterdam, Neth
Period6/28/947/1/94

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.