计数类至少和多项式时间层次结构一样困难

[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI:10.1109/SCT.1991.160238

Seinosuke Toda, M. Ogihara

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引用次数: 151

摘要

结果表明，在以下意义上，许多自然计数类至少与PH(多项式时间层次)一样难以计算:对于计数类的每K个，K(PH)中的每个集合都是多项式时间随机多一可约为K中的集合，具有双边指数小的误差概率。因此，这些计数类在计算上比PH更难，除非PH崩溃到一个有限的水平。其他一些后果也被显示出来。

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Counting classes are at least as hard as the polynomial-time hierarchy

It is shown that many natural counting classes are at least as computationally hard as PH (the polynomial-time hierarchy) in the following sense: for each K of the counting classes, every set in K(PH) is polynomial-time randomized many-one reducible to a set in K with two-sided exponentially small error probability. As a consequence, these counting classes are computationally harder than PH unless PH collapses to a finite level. Some other consequences are also shown.<>

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[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference

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