Geodesic
Finite automaton actions of free products of groups
Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 230-236

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It is shown that for groups $G$ and $H$ that act faithfully by finite state automorphisms on regular rooted trees their free product $G*H$ admits a faithful action by finite state automorphisms on some regular rooted tree.
Keywords: rooted tree, tree automorphism, finite automaton, free product. 
Mariia Fedorova; Andriy Oliynyk. Finite automaton actions of free products of groups. Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 230-236. http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a5/
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