Topological Entropy of Formal Languages

TL;DR

This paper introduces the concept of topological entropy for formal languages, providing a way to measure their complexity through automata theory, and computes this entropy for specific examples, linking simplicity to zero entropy.

Contribution

It defines topological entropy for formal languages and offers a method to compute it, connecting language complexity with automata properties.

Findings

Certain languages have zero entropy, indicating simplicity.

The entropy can be characterized via Myhill-Nerode relations.

Examples demonstrate the applicability of the entropy measure.

Abstract

We introduce the notion of topological entropy of a formal languages as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill-Nerode congruence relation, we are able to compute the topological entropies of certain example languages. Those examples suggest that the notion of a "simple" formal language coincides with the language having zero entropy.