Symbolic dynamics

TL;DR

This chapter explores the relationship between automata theory and symbolic dynamics, focusing on automata classes, shift embeddings, and the classification of sofic shifts via syntactic semigroups.

Contribution

It establishes new links between automata classes and symbolic dynamics, particularly in shift embeddings and shift classification methods.

Findings

Automata classes relate to shift embeddings

Syntactic semigroups classify sofic shifts

Connections between automata theory and symbolic dynamics clarified

Abstract

This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results on embeddings of shifts of finite type. The second one is the connection between syntactic semigroups and the classification of sofic shifts up to conjugacy.