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A set A is P-bi-immune if neither A nor its complement has an innnite 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 thatàlmost' every language in E is P-bi-immune, that is to say, almost every set recognizable in linear(More)
Ogiwara and Watanabe have recently shown that the hypothesis P 6 = NP implies that no polynomially sparse language is P btt-hard for NP. Their technique does not appear to allow signiicant relaxation of either the query bound or the sparseness criterion. It is shown here that a stronger hypothesis | namely, that NP does not have measure 0 in exponential(More)
Under the hypothesis that NP does not have p-measure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is shown that there is a language that is P T-complete (\Cook com-plete"), but not P m-complete (\Karp-Levin complete"), for NP. This conclusion, widely believed to be true, is not known to follow from P 6 = NP or other(More)
The two most important notions of fractal dimension are Hausdorff dimension, developed by Haus-dorff (1919), and packing dimension, developed independently by Tricot (1982) and Sullivan (1984). Both dimensions have the mathematical advantage of being defined from measures, and both have yielded extensive applications in fractal geometry and dynamical(More)
The two most important notions of fractal dimension are Hausdorff dimension, developed by Hausdorff (1919), and packing dimension, developed independently by Tricot (1982) and Sullivan (1984). Both dimensions have the mathematical advantage of being defined from measures, and both have yielded extensive applications in fractal geometry and dynamical(More)
We study the set of resource bounded Kolmogorov random strings: R t = fx j K t (x) jxjg for t a time constructible function such that t(n) 2 n 2 and t(n) 2 2 n O(1). We show that the class of sets that Tur-ing reduce to R t has measure 0 in EXP with respect to the resource-bounded measure introduced by 17]. From this we conclude that R t is not(More)