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arXiv · 2203.12963

Tree languages and branched groups

Laurent Bartholdi·Marialaura Noce
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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 $\omega$-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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Laurent Bartholdi, Marialaura Noce. 2022-03-24. Tree languages and branched groups. https://arxiv.org/abs/2203.12963

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