A list of applications of Stallings automata

TL;DR

This survey provides an updated overview of Stallings automata, emphasizing their applications in subgroup theory of free groups and focusing on algorithmic aspects, especially for finitely generated subgroups.

Contribution

It offers a comprehensive, accessible reference on Stallings automata, highlighting recent developments and algorithmic applications in subgroup analysis.

Findings

Enhanced algorithms for finitely generated subgroups

Broader results including non-finitely-generated cases

Updated references and applications in free group theory

Abstract

This survey is intended to be a fast (and reasonably updated) reference for the theory of Stallings automata and its applications to the study of subgroups of the free group, with the main accent on algorithmic aspects. Consequently, results concerning finitely generated subgroups have greater prominence in the paper. However, when possible, we try to state the results with more generality, including the usually overlooked non-(finitely-generated) case.