Groups and semigroups defined by colorings of synchronizing automata

Daniele D'Angeli, Emanuele Rodaro

Research output: Contribution to journalArticlepeer-review


In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to finitely generated synchronizing automata and characterize finite automata groups in terms of nilpotency of the corresponding DFA. Moreover, we present a decidable sufficient condition to have free semigroups in an automaton group. A series of examples and applications is widely discussed, in particular we show a way to color the de Bruijn automata into Mealy automata whose associated semigroups are free, and we present some structural results related to the associated groups.
Original languageEnglish
Pages (from-to)773-793
JournalInternational Journal of Algebra and Computation
Issue number6
Publication statusPublished - 2014

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Theoretical


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