Kolmogorov complexity as a combinatorial tool

TL;DR

This paper explores the use of Kolmogorov complexity as a combinatorial tool, demonstrating its application in proving the existence of winning strategies in combinatorial games where direct proofs are unknown.

Contribution

It introduces a novel application of Kolmogorov complexity to establish existence results in combinatorial game theory without explicit constructions.

Findings

Kolmogorov complexity can be used to prove existence of strategies

Application of complexity theory in combinatorial game analysis

Provides a new perspective on combinatorial proofs

Abstract

Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications where Kolmogorov complexity is used in a more subtle way. We provide one (somehow) surprising example where an existence of a winning strategy in a natural combinatorial game is proven (and no direct proof is known).