Geodesic
On free semigroups of automaton transformations
Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 248-259.

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It is established that the subset of free $k$-generated subsemigroups of the semigroup of all automaton transformations over a finite alphabet is a second category set (in the sense of the Baire category approach) in the set of all $k$-generated subsemigroups. A continuum series of pairs of automaton transformations each of which generates a free semigroup of rank two is indicated. A criterion is established for this semigroup to be a finite-automaton group. 
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A. S. Oliinyk. On free semigroups of automaton transformations. Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 248-259. http://geodesic.mathdoc.fr/item/MZM_1998_63_2_a8/

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