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On level-transitivity and exponential growth
Published 31 May 2016 in cs.FL and math.GR | (1605.09579v2)
Abstract: 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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