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 gametheoretic 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).
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 DOI:
 10.48550/arXiv.1003.4712
 arXiv:
 arXiv:1003.4712
 Bibcode:
 2010arXiv1003.4712M
 Keywords:

 Mathematics  Logic;
 Computer Science  Computer Science and Game Theory;
 Computer Science  Information Theory;
 68Q30;
 F.4.1
 EPrint:
 11 pages. Presented in 2009 at the conference on randomness in Madison.