Abstract
A natural interpretation of automorphisms of one-rooted trees as output automata permits the application of notions of growth and circuit structure in their study. New classes of groups are introduced corresponding to diverse growth functions and circuit structure. In the context of automorphisms of the binary tree, we discuss the structure of maximal 2-subgroups and the question of existence of free subgroups. Moreover, we construct Burnside 2-groups generated by automorphisms of the binary tree which are finite state, bounded, and acyclic.
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