柯尔莫哥洛夫生日悖论

Theor. Comput. Sci. Pub Date : 2022-08-24 DOI:10.48550/arXiv.2208.11237

Samuel Epstein

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引用次数: 0

摘要

我们证明了生日悖论的Kolmogorov复杂度变体。字符串的足够大的随机子集保证有两个成员x和y具有低K(x/y)。为了证明这一点，我们首先证明了有限集合的成员之间的最小条件Kolmogorov复杂度非常低，如果它们不是奇异的。奇异集与停止序列具有较高的互信息。

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The Kolmogorov Birthday Paradox

We prove a Kolmogorov complexity variant of the birthday paradox. Sufficiently sized random subsets of strings are guaranteed to have two members x and y with low K(x/y). To prove this, we first show that the minimum conditional Kolmogorov complexity between members of finite sets is very low if they are not exotic. Exotic sets have high mutual information with the halting sequence.

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Theor. Comput. Sci.

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