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Peer-reviewedCC BYMathematische Zeitschrift

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 ω 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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Cite

BibTeXRIS
BibTeX
@article{bartholdi2026tree,
  title = {{Tree languages and branched groups}},
  author = {Laurent Bartholdi and Marialaura Noce},
  journal = {Mathematische Zeitschrift},
  year = {2026},
  month = nov,
  doi = {10.1007/s00209-023-03249-y},
  eprint = {2203.12963},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05849730v1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Tree languages and branched groups
AU  - Laurent Bartholdi
AU  - Marialaura Noce
PY  - 2026
DA  - 2026/11/03
JO  - Mathematische Zeitschrift
DO  - 10.1007/s00209-023-03249-y
UR  - https://hal.science/hal-05849730v1
AB  - 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 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.
SN  - 0025-5874
SN  - 1432-1823
ER  -