Topological Entropy of Formal Languages

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.