Abstract An automaton (or a Mealy automaton)Aconsists of a tuple (Q,X,π,λ), in which Q is a set of states, X is a finite alphabet, π : Q×X → Q is a transition function and λ : Q×X → X is an output function. Among all the types of automata, we highlight finite invertible automaton in order to define an automata group. AspecialfamilyofautomatawhichhasfundamentalimportancetoourworkistheBellaterra automata family, first studied during the summer school in automata groups at the University of BarcelonainBellaterra, in2004(thisiswhytheseautomatareceivethisname); suchautomata are defined by wreath recursion. Onthispresentation,weconstructafamilyofautomata(theBellaterraautomata)withn≥4 states acting on a rooted binary tree generating free products of cyclic groups of order 2 by going through the concept of automata group. This study is based on the article [3].
References
[1] Meier, J., Groups, Graphs and Trees - An Introduction to the Geometry of Infinite Groups. London Mathematical Society Student Texts, Cambridge University Press, 2008. [2] Nekrashevych, V., Self-similar groups and their geometry, S˜ao Paulo Journal of Mathematical Sciences, volume 1, 2007. [3] Savchuk,D.andVorobets,Y.Automatageneratingfreeproductsofgroupsoforder2,JournalofAlgebra,volume 336, 2011.