Kolmogorov complexity in perspective

TL;DR

This paper surveys various approaches to information content, focusing on Kolmogorov complexity, its applications in randomness and classification, and recent developments in the field.

Contribution

It provides a comprehensive overview of Kolmogorov complexity, highlighting its historical development and recent applications in classification.

Findings

Kolmogorov complexity offers a rigorous mathematical framework for randomness.

Recent classification methods utilize Kolmogorov complexity for data analysis.

The survey connects classical and modern applications of information content measures.

Abstract

We survey the diverse approaches to the notion of information content: from Shannon entropy to Kolmogorov complexity. The main applications of Kolmogorov complexity are presented namely, the mathematical notion of randomness (which goes back to the 60's with the work of Martin-Lof, Schnorr, Chaitin, Levin), and classification, which is a recent idea with provocative implementation by Vitanyi and Cilibrasi.