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 cc-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 - 1994 |
| Externally published | Yes |
| Event | Proceedings of the 9th Annual Structure in Complexity Theory Conference - Amsterdam, Neth Duration: Jun 28 1994 → Jul 1 1994 |
Other
| Other | Proceedings of the 9th Annual Structure in Complexity Theory Conference |
|---|---|
| City | Amsterdam, Neth |
| Period | 6/28/94 → 7/1/94 |
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ASJC Scopus subject areas
- Engineering(all)
Cite this
Polynomial-time membership comparable sets. / Ogihara, Mitsunori.
Proceedings of the IEEE Annual Structure in Complexity Theory Conference. ed. / Anon. Publ by IEEE, 1994. p. 2-11.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Polynomial-time membership comparable sets
AU - Ogihara, Mitsunori
PY - 1994
Y1 - 1994
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 cc-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 cc-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
SP - 2
EP - 11
BT - Proceedings of the IEEE Annual Structure in Complexity Theory Conference
A2 - Anon, null
PB - Publ by IEEE
ER -