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)

Cite this

@inproceedings{7c034f92ea0243a3bb899428218c4870,

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.",

author = "Mitsunori Ogihara",

year = "1994",

month = dec,

day = "1",

language = "English (US)",

isbn = "0818656727",

series = "Proceedings of the IEEE Annual Structure in Complexity Theory Conference",

publisher = "Publ by IEEE",

pages = "2--11",

editor = "Anon",

booktitle = "Proceedings of the IEEE Annual Structure in Complexity Theory Conference",

note = "Proceedings of the 9th Annual Structure in Complexity Theory Conference ; Conference date: 28-06-1994 Through 01-07-1994",

}

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.

UR - http://www.scopus.com/inward/record.url?scp=0028573649&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028573649&partnerID=8YFLogxK

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 -

Polynomial-time membership comparable sets

Abstract

Publication series

Other

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this