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The Kolmogorov Birthday Paradox

2022/08/24 by Epstein, Samuel
#Computational Complexity (cs.CC) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.2208.11237

Abstract

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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