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 .
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