Oracles that compute values

Stephen Fenner, Steven Homer, Mitsunori Ogihara, Alan Selman

Research output: Contribution to journalArticle

15 Scopus citations

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, for every k, k adaptive (nonadaptive) queries to NPMV are different than k + 1 adaptive (nonadaptive) queries to NPMV. 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)
Pages (from-to)1043-1065
Number of pages23
JournalSIAM Journal on Computing
Volume26
Issue number4
DOIs
StatePublished - Aug 1997
Externally publishedYes

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Keywords

  • Boolean hierarchy
  • Bounded query classes
  • Complexity classes
  • Computational complexity
  • Multivalued functions
  • NPMV
  • Relativized computation

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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