Date: 03 Jun 2005

On random hard sets for NP

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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.