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On random hard sets for NP

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Algorithms and Computation (ISAAC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 834))

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Abstract

The problem of whether NP has a random hard set (i.e., a set in RAND) is investigated. We show that for all recursive oracle A such that PA ≠ NPA, NPA has no hard set in RAND. On the other hand, we also show that for almost all oracle A, PA ≠ NPA and NPA has a hard set in RAND.

Part of this research was done while the second author was visiting Department of Mathematics, University of California at Santa Barbara. This research is supported in part by NSF grant CCR-9302057.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, University of California, 93106, Santa Barbara, CA, USA

    Ronald V. Book

  2. Dept. of Computer Science, Tokyo Institute of Technology, Meguro-ku Ookayama, 152, Tokyo, Japan

    Osamu Watanabe

Authors
  1. Ronald V. Book
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  2. Osamu Watanabe
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Ding-Zhu Du Xiang-Sun Zhang

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© 1994 Springer-Verlag Berlin Heidelberg

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Book, R.V., Watanabe, O. (1994). On random hard sets for NP. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_165

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  • DOI: https://doi.org/10.1007/3-540-58325-4_165

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58325-7

  • Online ISBN: 978-3-540-48653-4

  • eBook Packages: Springer Book Archive

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