电路下界坍缩相对复杂性类

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-05-04 DOI:10.1109/CCC.1999.766280

R. Beigel, Alexis Maciel

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引用次数: 5

摘要

自从M. Furst et al.(1984)发表了将AC/sup 0/与多项式层次结构联系起来的开创性论文以来，众所周知，电路下界允许您构建分离复杂性类的预言机。我们展示了类似的电路下界允许您构建分解复杂类的预言器。例如，基于hasad的奇偶下界，我们构造了一个P=PH/spl sub//spl oplus/P=EXP的oracle。

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Circuit lower bounds collapse relativized complexity classes

Since the publication of M. Furst et al. (1984) seminal paper connecting AC/sup 0/ with the polynomial hierarchy, it has been well known that circuit lower bounds allow you to construct oracles that separate complexity classes. We show that similar circuit lower bounds allow you to construct oracles that collapse complexity classes. For example, based on Hastad's parity lower bound, we construct an oracle such that P=PH/spl sub//spl oplus/P=EXP.

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Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)

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