The concept of self-similar automata over a changing alphabet and lamplighter groups generated by such automata
Generalizing the idea of self-similar groups defined by Mealy automata, we introduce the notion of a self-similar automaton and a self-similar group over a changing alphabet. We show that every finitely generated residually-finite group is self-similar over an arbitrary unbounded changing alphabet. We construct some naturally defined self-similar automaton representations over an unbounded changing alphabet for any lamplighter group K Z with an arbitrary finitely generated (finite or infinite) abelian group K. (C) 2013 Elsevier B.V. All rights reserved.
changing alphabet lamplighter group rooted tree time-varying automaton group generated by an automaton