The concept of duality for automata over a changing alphabet and generation of a free group by such automata

Abstract

In the paper, we deal with the notion of an automaton over a changing alphabet, which generalizes the concept of a Mealy-type automaton. We modify the methods based on the idea of a dual automaton and its action used by B. Steinberg et al. (2011) and M. Vorobets and Ya. Vorobets (2007,2010) and adapt them to automata over a changing alphabet. We show that this modification provides some naturally defined automaton representations of a free nonabelian group by a 2-state automaton over a changing alphabet.

Cited by in corpus (3)

• The concept of self-similar automata over a changing alphabet and lamplighter groups generated by such automata
• On groups generated by bi-reversible automata: the two-state case over a changing alphabet
• The classification of abelian groups generated by time-varying automata and by Mealy automata over the binary alphabet