On using oracles that compute values

  • Stephen Fenner
  • Steve Homer
  • Mitsunori Ogiwara
  • Alan L. Selman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


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. 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. 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. 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.


Polynomial Time Partial Function Input String Satisfying Assignment Polynomial Hierarchy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Stephen Fenner
    • 1
  • Steve Homer
    • 2
  • Mitsunori Ogiwara
    • 3
  • Alan L. Selman
    • 4
  1. 1.Dept. of Computer ScienceUniversity of Southern MainePortland
  2. 2.Dept. of Computer ScienceBoston UniversityBoston
  3. 3.Dept. of Computer ScienceUniversity of Electro-CommunicationsTokyoJapan
  4. 4.Dept. of Computer ScienceSUNY at BuffaloBuffalo

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