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- W2295289317 abstract "M. Blum and R. Impagliazzo (Proc. 28th IEEE Symposium on Foundations of Computer Science, pp. 118-126, 1987), using techniques of Hartmanis and Hemachandra (1991) and Rackoff (1982), showed that if P = NP then P(G) = NP(G)/spl cap/co-NP(G) = UP(G), where G is a generic oracle. They left open the question as to whether these collapses occur at higher levels of the polynomial-time hierarchy. We give a surprising negative answer to this question. We show that relative to any generic oracle G and for any k/spl ges/ 2, there exists a tally set in U/spl Deltasub ksup P/(G)/spl capspl Pisub ksup P/(G) but not in /spl Deltasub ksup P/(G). An immediate corollary is that generic oracles separate /spl Sigmasub ksup Pspl capspl Pisub ksup P/ and /spl Deltasub ksup P/. We also show that related results hold for type-2 complexity. >" @default.
- W2295289317 created "2016-06-24" @default.
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- W2295289317 date "2002-12-17" @default.
- W2295289317 modified "2023-09-23" @default.
- W2295289317 title "Generic separations" @default.
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- W2295289317 doi "https://doi.org/10.1109/sct.1994.315809" @default.
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