NP-sets are Co-NP-immune relative to a random oracle

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ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Year:
1995

Citing 0
Cited 2

Strong Reductions and Immunity for Exponential Time

STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Resource bounded immunity and simplicity

Theoretical Computer Science

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Abstract

Abstract: We prove that the class NP has Co-NP-immune sets relative to a random oracle. Moreover, we prove that, relative to a random oracle, there are L/spl isin/P and NP-set L/sub 1//spl sub/L such that both L/sub 1/ and L|L/sub 1/ are infinite, L/sub 1/ has no infinite Co-NP-subsets and L|L/sub 1/ has no infinite NP-subsets. The second theorem implies both the first theorem and the theorem in Vereshchagin (1993) that Co-NP has NP-immune sets relative to a random oracle.