Entropy for symbolic dynamics with overlapping alphabets

TL;DR

This paper introduces a new entropy concept for symbolic dynamics with overlapping alphabets, providing methods for bounds and linking it to the entropy of associated dynamical systems.

Contribution

It defines entropy for nontransitively overlapping shift spaces and establishes its relation to standard shift entropies and dynamical system entropy bounds.

Findings

Entropy equals a limit of standard shift entropies

Provides techniques for lower bounds of entropy

Entropy bounds the topological entropy of related dynamical systems

Abstract

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of entropies of (standard) full shifts. When a shift space with overlaps arises as a model for a discrete dynamical system with a finite set of overlapping neighborhoods, the entropy gives a lower bound for the topological entropy of the dynamical system.