Dmytro Savchuk, Binghamton University

Abstract:
We construct a family of automata with n states, n>3, acting on a rooted binary tree that generate the free products of cyclic groups of order 2. This family generalizes the so-called Bellaterra automaton, which is a 3-state automaton generating the free product of 3 groups of order 2. I will give short exposition of the history of this question, explain the construction and main ideas behind the proof. This is a joint result with Yaroslav Vorobets of Texas A&M University.