TY - GEN

T1 - Polynomial-time membership comparable sets

AU - Ogihara, Mitsunori

PY - 1994/12/1

Y1 - 1994/12/1

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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M3 - Conference contribution

AN - SCOPUS:0028573649

SN - 0818656727

T3 - Proceedings of the IEEE Annual Structure in Complexity Theory Conference

SP - 2

EP - 11

BT - Proceedings of the IEEE Annual Structure in Complexity Theory Conference

A2 - Anon, null

PB - Publ by IEEE

T2 - Proceedings of the 9th Annual Structure in Complexity Theory Conference

Y2 - 28 June 1994 through 1 July 1994

ER -