On the conjugacy problem for finite-state automorphisms of regular rooted trees

Details On the conjugacy problem for finite-state automorphisms of regular rooted trees On the conjugacy problem for finite-state automorphisms of regular rooted trees

2010-11-09

arxiv.org/abs/1011.2227v1

Mathematics

Group Theory

23 pages, 2 figures

Scientific paper

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 these conditions are satisfied by bounded automorphisms and establish that the (simultaneous) conjugacy problem in the group of bounded automata is decidable.

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