Simple Classes of Automatic Structures

TL;DR

This paper explores specific subclasses of automatic structures, focusing on polynomial growth and Presburger structures, providing algebraic characterizations of groups and equivalence structures within these classes.

Contribution

It introduces algebraic characterizations for automatic structures of polynomial growth and Presburger structures, advancing understanding of their algebraic properties.

Findings

Algebraic characterizations of groups in these classes

Descriptions of equivalence structures within these subclasses

Insights into the structure of automatic structures with polynomial growth

Abstract

We study two subclasses of the class of automatic structures: automatic structures of polynomial growth and Presburger structures. We present algebraic characterisations of the groups and the equivalence structures in these two classes.