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On level-transitivity and exponential growth

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Abstract

We prove that if the group generated by an invertible and reversible Mealy automaton acts level-transitively on a regular rooted tree, then the semigroup generated by the dual automaton has exponential growth, hence giving a decision procedure of exponential growth for a restricted family of automaton (semi)groups.

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Authors and Affiliations

  1. Sorbonne Paris Cité, IRIF, UMR 8243 CNRS, Univ Paris Diderot, 75013, Paris, France

    Ines Klimann

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  1. Ines Klimann
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Correspondence to Ines Klimann.

Additional information

Communicated by Benjamin Steinberg.

This work was partially supported by the French Agence Nationale pour la Recherche, through the Project MealyM ANR-JS02-012-01.

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Klimann, I. On level-transitivity and exponential growth. Semigroup Forum 95, 441–447 (2017). https://doi.org/10.1007/s00233-016-9824-7

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  • DOI: https://doi.org/10.1007/s00233-016-9824-7

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