Exploring the Topological Entropy of Formal Languages

TL;DR

This paper introduces the concept of topological entropy for formal languages and automata, exploring its properties and bounds, especially for languages accepted by deterministic epsilon-free push-down automata with multiple stacks.

Contribution

It defines topological entropy for formal languages and automata, demonstrating its surjectivity and establishing bounds for certain classes of automata.

Findings

Entropy function is surjective.

Bounds on entropy for languages accepted by deterministic epsilon-free push-down automata.

Topological entropy provides a new measure for formal language complexity.

Abstract

We introduce the notions of topological entropy of a formal language and of a topological automaton. We show that the entropy function is surjective and bound the entropy of languages accepted by deterministic {\epsilon}-free push-down automata with an arbitrary amount of stacks.