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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)
Acknowledgements I w ant to thank specially two people, Jos e Luis Balcc azar and Jack Lutz. Without their help and encouragement this dissertation would never have been written. Jos e Luis Balcc azar was my advisor and taught m e m o s t o f w h a t I k n o w about Structural Complexity, showing me with his example how to do research. I visited Jack Lutz(More)