Chapter

Algorithms and Computation

Volume 834 of the series Lecture Notes in Computer Science pp 47-55

Date:

On random hard sets for NP

  • Ronald V. BookAffiliated withDept. of Mathematics, University of California
  • , Osamu WatanabeAffiliated withDept. of Computer Science, Tokyo Institute of Technology

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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.