Three Lectures on Automatic Structures

TL;DR

This paper reviews various types of automatic structures, including those based on word, tree, Buchi, and Rabin automata, highlighting their representations and properties in the context of automata theory.

Contribution

It provides an overview of different models of automatic structures and discusses their relationships and properties, serving as an introduction to this active research area.

Findings

Automatic structures can be represented by various automata models.

Properties of automatic structures are a focus of ongoing research.

Different automata types process different kinds of infinite or finite data.

Abstract

This paper grew out of three tutorial lectures on automatic structures given by the first author at the Logic Colloquium 2007. We discuss variants of automatic structures related to several models of computation: word automata, tree automata, Buchi automata, and Rabin automata. Word automata process finite strings, tree automata process finite labeled trees, Buchi automata process infinite strings, and Rabin automata process infinite binary labeled trees. Automatic structures are mathematical objects which can be represented by (word, tree, Buchi, or Rabin) automata. The study of properties of automatic structures is a relatively new and very active area of research.