AUTOMATA OVER A BINARY ALPHABET GENERATING FREE GROUPS OF EVEN RANK
Benjamin Steinberg, Mariya Vorobets, Yaroslav Bogdanovich Vorobets · International Journal of Algebra and Computation · 2011
We construct automata over a binary alphabet with 2n states, n ≥ 2, whose states freely generate a free group of rank 2n. Combined with previous work, this shows that a free group of every finite rank can be generated by finite automata over a binary alphabet. We also construct free products of cyclic groups of order two via such automata.