On using oracles that compute values

Stephen Fenner, Steve Homer, Mitsunori Ogihara, Alan L. Selman

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

7 Citations (Scopus)

Abstract

This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomial-time reducibilities, it is shown that 1. A multivalued partial function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable via 2k-1 nonadaptive queries to NPMV. 2. A characteristic function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable with k adaptive queries to NP. 3. Unless the Boolean hierarchy collapses, k adaptive (nonadaptive) queries to NPMV is different than k+1 adaptive (nonadaptive) queries to NPMV for every k. Nondeterministic reducibilities, lowness and the difference hierarchy over NPMV are also studied. The difference hierarchy for partial functions does not collapse unless the Boolean hierarchy collapses, but, surprisingly, the levels of the difference and bounded query hierarchies do not interleave (as is the case for sets) unless the polynomial hierarchy collapses.

Original languageEnglish (US)
Title of host publicationSTACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
PublisherSpringer Verlag
Pages399-407
Number of pages9
Volume665 LNCS
ISBN (Print)9783540565031
StatePublished - 1993
Externally publishedYes
Event10th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1993 - Wurzburg, Germany
Duration: Feb 25 1993Feb 27 1993

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume665 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1993
CountryGermany
CityWurzburg
Period2/25/932/27/93

Fingerprint

Polynomial time
Polynomials
Query
Partial
Reducibility
Multivalued
If and only if
Polynomial Hierarchy
Complexity Classes
Characteristic Function
Hierarchy

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Fenner, S., Homer, S., Ogihara, M., & Selman, A. L. (1993). On using oracles that compute values. In STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings (Vol. 665 LNCS, pp. 399-407). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 665 LNCS). Springer Verlag.

On using oracles that compute values. / Fenner, Stephen; Homer, Steve; Ogihara, Mitsunori; Selman, Alan L.

STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings. Vol. 665 LNCS Springer Verlag, 1993. p. 399-407 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 665 LNCS).

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

Fenner, S, Homer, S, Ogihara, M & Selman, AL 1993, On using oracles that compute values. in STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings. vol. 665 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 665 LNCS, Springer Verlag, pp. 399-407, 10th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1993, Wurzburg, Germany, 2/25/93.
Fenner S, Homer S, Ogihara M, Selman AL. On using oracles that compute values. In STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings. Vol. 665 LNCS. Springer Verlag. 1993. p. 399-407. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Fenner, Stephen ; Homer, Steve ; Ogihara, Mitsunori ; Selman, Alan L. / On using oracles that compute values. STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings. Vol. 665 LNCS Springer Verlag, 1993. pp. 399-407 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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