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Tree languages and branched groups

2022/03/24 by Laurent Bartholdi, Marialaura Noce, Bartholdi, Laurent +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #20E08 #20F10 #68Q45 #Cellular Automata and Applications #DNA and Biological Computing #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2203.12963

openalex publication_date 2022/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the portraits of isometries of rooted trees - the labelling of the tree, at each vertex, by the permutation of its descendants - in terms of languages. We characterize regularly branched self-similar groups in terms of ω-regular languages. We deduce the algorithmic decidability of some problems, such as the comparison of regularly branched contracting groups, and their orbit structure on the boundary of the rooted tree.

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