On orbits and the finiteness of bounded automaton groups
Ievgen Bondarenko, Jan Philipp Wächter · International Journal of Algebra and Computation · 2021
We devise an algorithm which, given a bounded automaton [Formula: see text], decides whether the group generated by [Formula: see text] is finite. The solution comes from a description of the infinite sequences having an infinite [Formula: see text]-orbit using a deterministic finite-state acceptor. This acceptor can also be used to decide whether the bounded automaton acts level-transitively.