On level-transitivity and exponential growth
Formal Languages and Automata Theory
2016-08-18 v2 Group Theory
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.
Cite
@article{arxiv.1605.09579,
title = {On level-transitivity and exponential growth},
author = {Ines Klimann},
journal= {arXiv preprint arXiv:1605.09579},
year = {2016}
}