The Kolmogorov Birthday Paradox

Samuel Epstein

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arXiv · 2208.11237

The Kolmogorov Birthday Paradox

Samuel Epstein

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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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Samuel Epstein. 2022-08-24. The Kolmogorov Birthday Paradox. https://arxiv.org/abs/2208.11237

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