Date: 03 Jun 2005

On random hard sets for NP

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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.