随机序列的独立性
Independence Properties of Algorithmically Random Sequences
摘要：
有界Kolmogorov-Loveland选择规则是一种自适应策略，用于递归地选择无限二进制序列的子序列;这样的子序列可以被解释为时间有界图灵机的查询序列。本文证明了：若A是算法随机序列，A_0是由有界Kolmogorov-Loveland选择规则从A中选出的，A_1表示A的未选比特序列，则A_1与A_0无关，即A_1相对于A_0是算法随机的.这个结果已经被Kautz和Miltersen [1]用来证明相对于随机预言，NP不具有p-测度零（在Lutz [2]的意义下）。[1]S. M. Kautz和P.B.米尔特森相对于随机预言机，NP并不小。计算机与系统科学杂志，53：235-250，1996。[2]J. H.卢茨几乎到处都是高度非均匀复杂性。计算机与系统科学杂志，44：220-258，1992。
英文摘要：
A bounded Kolmogorov-Loveland selection rule is an adaptive strategy for recursively selecting a subsequence of an infinite binary sequence; such a subsequence may be interpreted as the query sequence of a time-bounded Turing machine. In this paper we show that if A is an algorithmically random sequence, A_0 is selected from A via a bounded Kolmogorov-Loveland selection rule, and A_1 denotes the sequence of nonselected bits of A, then A_1 is independent of A_0; that is, A_1 is algorithmically random relative to A_0. This result has been used by Kautz and Miltersen [1] to show that relative to a random oracle, NP does not have p-measure zero (in the sense of Lutz [2]). [1] S. M. Kautz and P. B. Miltersen. Relative to a random oracle, NP is not small. Journal of Computer and System Sciences, 53:235-250, 1996. [2] J. H. Lutz. Almost everywhere high nonuniform complexity. Journal of Computer and System Sciences, 44:220-258, 1992.
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