Geodesic
Post-critically finite self-similar groups
Algebra and discrete mathematics, no. 4 (2003), pp. 21-32.

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We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is contracting. 
@article{ADM_2003_4_a3,
     author = {E. Bondarenko and V. Nekrashevych},
     title = {Post-critically finite self-similar groups},
     journal = {Algebra and discrete mathematics},
     pages = {21--32},
     publisher = {mathdoc},
     number = {4},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2003_4_a3/}
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E. Bondarenko; V. Nekrashevych. Post-critically finite self-similar groups. Algebra and discrete mathematics, no. 4 (2003), pp. 21-32. http://geodesic.mathdoc.fr/item/ADM_2003_4_a3/