Complicated complementations

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.1999.766281

H. Buhrman, L. Torenvliet

引用次数: 6

Abstract

Kolmogorov complexity has proven to be a very useful tool in simplifying and improving proofs that use complicated combinatorial arguments. Using Kolmogorov complexity for oracle construction, we obtain separation results that are much stronger than separations obtained previously even with the use of very complicated combinatorial arguments. Moreover the use of Kolmogorov arguments almost trivializes the construction itself: In particular we construct relativized worlds where: 1. NP/spl cap/CoNP/spl isin/P/poly. 2. NP has a set that is both simple and NP/spl cap/CoNP-immune. 3. CoNP has a set that is both simple and NP/spl cap/CoNP-immune. 4. /spl Pi//sub 2//sup p/ has a set that is both simple and /spl Pi//sub 2//sup p//spl cap//spl Sigma//sup 2p/-immune.

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复杂的互补

在简化和改进使用复杂组合论证的证明方面，Kolmogorov复杂度已被证明是一个非常有用的工具。使用Kolmogorov复杂度来构造oracle，我们得到的分离结果比以前使用非常复杂的组合参数得到的分离结果强得多。此外，Kolmogorov论证的使用几乎使构造本身变得无足轻重:特别是我们构造相对化的世界，其中:1。NP/spl cap/CoNP/spl isin/P/poly2. NP有一组既简单又NP/spl cap/ cp免疫的集合。3.CoNP有一组既简单又不受NP/spl限制/CoNP影响的集合。4. /spl Pi// sub2 //sup p/有一个集合，它既简单又/spl Pi// sub2 //sup p//spl cap//spl Sigma//sup 2p/-免疫。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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