Topological arguments for Kolmogorov complexity

TL;DR

This paper explores how basic topological principles, like the simple connectivity of the disk, can be applied to derive new results and properties in Kolmogorov complexity, demonstrating the interplay between topology and algorithmic information theory.

Contribution

It introduces novel applications of elementary topological arguments to establish nontrivial properties in Kolmogorov complexity, bridging topology and algorithmic information theory.

Findings

Topological methods can derive properties of Kolmogorov complexity.

Simple topological facts are sufficient for constructing strings with specific algorithmic properties.

Topological arguments provide new insights into the structure of Kolmogorov complexity.

Abstract

We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties.