On level-transitivity and exponential growth
Résumé
We prove that if the group generated by a 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 semigroups.
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a_link_between_level_transitivity_and_exponential_growth_hal.pdf (125.25 Ko)
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