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arXiv · 1003.4712

Game interpretation of Kolmogorov complexity

Andrej A. Muchnik·Ilya Mezhirov·Alexander Shen·Nikolay Vereshchagin
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Abstract

The Kolmogorov complexity function K can be relativized using any oracle A, and most properties of K remain true for relativized versions. In section 1 we provide an explanation for this observation by giving a game-theoretic interpretation and showing that all "natural" properties are either true for all sufficiently powerful oracles or false for all sufficiently powerful oracles. This result is a simple consequence of Martin's determinacy theorem, but its proof is instructive: it shows how one can prove statements about Kolmogorov complexity by constructing a special game and a winning strategy in this game. This technique is illustrated by several examples (total conditional complexity, bijection complexity, randomness extraction, contrasting plain and prefix complexities).

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BibTeXRIS

Andrej A. Muchnik, Ilya Mezhirov, Alexander Shen, Nikolay Vereshchagin. 2010-03-24. Game interpretation of Kolmogorov complexity. https://arxiv.org/abs/1003.4712

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