On level-transitivity and exponential growth
Ines Klimann (IRIF)
TL;DR
This paper establishes a connection between level-transitivity of groups generated by Mealy automata and exponential growth of the associated semigroups, providing a decision procedure for a specific class of automaton semigroups.
Contribution
It proves that level-transitivity implies exponential growth in the dual automaton semigroup, offering a new criterion for analyzing automaton semigroup growth.
Findings
Level-transitivity implies exponential growth in the dual automaton semigroup.
Provides a decision procedure for exponential growth in a restricted class of automaton semigroups.
Establishes a link between automaton group actions and semigroup growth properties.
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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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Mathematical Dynamics and Fractals