通用的分离

Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1996-02-01 DOI:10.1109/SCT.1994.315809

L. Fortnow, T. Yamakami

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引用次数: 9

摘要

M. Blum和R. Impagliazzo (Proc. 28 IEEE Symposium on Foundations of Computer Science, pp. 118-126, 1987)，利用Hartmanis和Hemachandra(1991)和Rackoff(1982)的技术，证明了如果P = NP，那么P(G) = NP(G)/spl cap/co-NP(G) = UP(G)，其中G是一个泛型oracle。他们留下了一个悬而未决的问题，即这些崩溃是否发生在多项式时间层次的更高层次上。对于这个问题，我们给出了一个令人惊讶的否定答案。我们证明了对于任意泛型oracle G和任意k/spl ges/ 2，在U/spl Deltasub ksup P/(G)/spl capspl Pisub ksup P/(G)中存在一个计数集，而在/spl Deltasub ksup P/(G)中不存在计数集。一个直接的推论是，通用的oracle将/spl Sigmasub ksup Pspl capspl Pisub ksup P/和/spl Deltasub ksup P/分开。我们还表明，相关结果适用于type-2复杂度

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Generic separations

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.<>

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Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory

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