Date: 28 May 2005

P-generic sets

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Abstract

We introduce the notion of a p-generic set. P-generic sets automatically have all properties which can be enforced by usual diagonalizations over polynomial time computable sets and functions. We prove that there are recursive — in fact exponential time computable — p-generic sets. The existence of p-generic sets in NP is shown to be oracle dependent, even under the assumption that PNP.