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Bounded query classes and the difference hierarchy

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Abstract

LetA be any nonrecursive set. We define a hierarchy of sets (and a corresponding hierarchy of degrees) that are reducible toA based on bounding the number of queries toA that an oracle machine can make. WhenA is the halting problemK our hierarchy of sets interleaves with the difference hierarchy on the r.e. sets in a logarithmic way; this follows from a tradeoff between the number of parallel queries and the number of serial queries needed to compute a function with oracleK.

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Author notes

  1. Richard Beigel

    Present address: Department of Computer Science, Yale University, 51 Prospect Street, P.O.Box 2158, 06520, Yale Station, New Haven, CT, USA

Authors and Affiliations

  1. Department of Computer Science, The Johns Hopkins University, 21218, Baltimore, MD, USA

    Richard Beigel

  2. Department of Computer Science, Institute for Advanced Studies, University of Maryland, 20742, College Park, MD, USA

    William I. Gasarch

  3. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 60680, Chicago, IL, USA

    Louise Hay

Authors
  1. Richard Beigel
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  2. William I. Gasarch
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  3. Louise Hay
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Additional information

Supported in part by NSF grant CCR-8808949. Part of this work was completed while this author was a student at Stanford University supported by fellowships from the National Science Foundation and from the Fannie and John Hertz Foundation

Supported in part by NSF grant CCR-8803641

Part of this work was completed while this author was on sabbatical leave at the University of California, Berkeley

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Beigel, R., Gasarch, W.I. & Hay, L. Bounded query classes and the difference hierarchy. Arch Math Logic 29, 69–84 (1989). https://doi.org/10.1007/BF01620618

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  • DOI: https://doi.org/10.1007/BF01620618

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