Geodesic
On the conjugacy problem for finite-state automorphisms of regular rooted trees (with an appendix by Raphaël M. Jungers)
Ievgen V. Bondarenko1 ; Natalia V. Bondarenko2 ; Said N. Sidki3 ; Flavia R. Zapata4
1Taras Shevchenko National University of Kyiv, Ukraine
2Kyiv National University of Construction and Architecture, Ukraine
3Universidade de Brasília, Brazil
4Universidade de Brasília, Brasília, Brazil
Groups, geometry, and dynamics, Tome 7 (2013) no. 2, pp. 323-355

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DOI

We study the conjugacy problem in the automorphism group Aut(T) of a regular rooted tree T and in its subgroup FAut(T) of finite-state automorphisms. We show that under the contracting condition and the finiteness of what we call the orbit-signalizer, two finite-state automorphisms are conjugate in Aut(T) if and only if they are conjugate in FAut(T), and that this problem is decidable. We prove that both conditions are satisfied by bounded automorphisms and establish that the (simultaneous) conjugacy problem in the group of bounded automata is decidable.
DOI : 10.4171/ggd/184
Classification : 20-XX, 00-XX
Mots-clés : Automorphism of a rooted tree, conjugacy problem, finite-state automorphism, finite automaton, bounded automaton

Ievgen V. Bondarenko  1   ; Natalia V. Bondarenko  2   ; Said N. Sidki  3   ; Flavia R. Zapata  4

1 Taras Shevchenko National University of Kyiv, Ukraine
2 Kyiv National University of Construction and Architecture, Ukraine
3 Universidade de Brasília, Brazil
4 Universidade de Brasília, Brasília, Brazil 
Ievgen V. Bondarenko; Natalia V. Bondarenko; Said N. Sidki; Flavia R. Zapata. On the conjugacy problem for finite-state automorphisms of regular rooted trees (with an appendix by Raphaël M. Jungers). Groups, geometry, and dynamics, Tome 7 (2013) no. 2, pp. 323-355. doi: 10.4171/ggd/184
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     author = {Ievgen V. Bondarenko and Natalia V. Bondarenko and Said N. Sidki and Flavia R. Zapata},
     title = {On the conjugacy problem for finite-state automorphisms of regular rooted trees (with an appendix by {Rapha\"el} {M.} {Jungers)}},
     journal = {Groups, geometry, and dynamics},
     pages = {323--355},
     year = {2013},
     volume = {7},
     number = {2},
     doi = {10.4171/ggd/184},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/184/}
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