On random hard sets for NP

  • Ronald V. Book
  • Osamu Watanabe
Conference paper

DOI: 10.1007/3-540-58325-4_165

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


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.


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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Ronald V. Book
    • 1
  • Osamu Watanabe
    • 2
  1. 1.Dept. of MathematicsUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Dept. of Computer ScienceTokyo Institute of TechnologyTokyoJapan

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