A list of applications of Stallings automata
Jordi Delgado, Enric Ventura

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.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Advanced Operator Algebra Research
