# Algorithmic Search in Group Theory

## TL;DR

This paper introduces a Kolmogorov complexity-based random search method for group theory problems, demonstrating its theoretical effectiveness and practical heuristic approximations with experimental support.

## Contribution

It proposes a novel search approach using Kolmogorov complexity for group theory, combining theoretical guarantees with heuristic methods and experimental validation.

## Key findings

- The method is provably effective in theory.
- Heuristic approximations perform well in practice.
- Experimental evidence supports the approach's viability.

## Abstract

A method of random search based on Kolmogorov complexity is proposed and applied to two search problems in group theory. The method is provably effective but not practical, so the applications involve heuristic approximations. Perhaps surprisingly, these approximations seem to work. Some experimental evidence is presented.