English

Infinite finitely generated automata semigroups have infinite orbits

Group Theory 2018-01-31 v1

Abstract

We prove that the semigroup generated by a finite state Mealy automaton A=(Q,A,τ)\mathcal{A}=(Q,A,\tau) is infinite if and only if there exists some right-infinite word in the alphabet AA with infinite orbit.

Keywords

Cite

@article{arxiv.1801.10009,
  title  = {Infinite finitely generated automata semigroups have infinite orbits},
  author = {Dominik Francoeur},
  journal= {arXiv preprint arXiv:1801.10009},
  year   = {2018}
}

Comments

8 pages, 4 figures

R2 v1 2026-06-23T00:03:39.075Z