Game interpretation of Kolmogorov complexity
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).
Keywords
Cite
@article{arxiv.1003.4712,
title = {Game interpretation of Kolmogorov complexity},
author = {Andrej A. Muchnik and Ilya Mezhirov and Alexander Shen and Nikolay Vereshchagin},
journal= {arXiv preprint arXiv:1003.4712},
year = {2010}
}
Comments
11 pages. Presented in 2009 at the conference on randomness in Madison.