Presentations of symbolic dynamical systems by labelled directed graphs (Notes for a "mini-cours", SDA2, Paris 4-5 October 2007)

TL;DR

This paper develops a general theory for representing symbolic dynamical systems, specifically subshifts, using labelled directed graphs, including compact and countable graphs, and explores synchronization properties.

Contribution

It introduces new methods for representing subshifts with labelled graphs, expanding the understanding of their structure and synchronization features.

Findings

Presented a framework for representing subshifts with compact graphs.

Analyzed synchronization properties leading to countable graph presentations.

Extended the theory of symbolic dynamical systems with graph-based representations.

Abstract

We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable graphs.