Almost every set in exponential time is P-Bi-Immune
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A set A is P-bi-immune if neither A nor its complement has an infinite subset in P. We investigate here the abundance of P-bi-immune languages in linear-exponential time (E). We prove that the class of P-bi-immune sets has measure 1 in E. This implies that "almost" every language in E is P-bi-immune. A bit further, we show that every p-random (pseudorandom) language is E-bi-immune. Regarding the existence of P-bi-immune sets in N P, we show that if N P does not have measure 0 in E, then N P contains a P-bi-immune set. Another consequence is that the class of =[super p sub m] -complete languages for E has measure 0 in E. In contrast, it is shown that in E, and even in REC, the class of P-bi-immune languages lacks the property of Baire (the Baire category analogue of Lebesgue measurability).
CitationMayordomo, E. Almost every set in exponential time is P-Bi-Immune. 1991.
Is part ofLSI-91-46