Randomness, Information, and Complexity

TL;DR

This paper reviews various measures of complexity and information, emphasizing the challenges in distinguishing complex from disordered systems and analyzing sequence classification and forecasting.

Contribution

It provides a comprehensive review of complexity and information measures, highlighting their limitations and applications to sequence analysis.

Findings

Not all complexity measures align with intuitive notions.

Distinguishing complex from disordered systems is challenging.

Some measures effectively quantify classification and forecasting difficulty.

Abstract

We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that one should not expect a unique observable of complexity. One of the main problems is to distinguish complex from disordered systems. This and the fact that complexity is closely related to information requires that we also give a review of information measures. We finally concentrate on quantities which measure in some way or other the difficulty of classifying and forecasting sequences of discrete symbols, and study them in simple examples.