On the number of automorphisms of non-cyclic automata

Abstract

Various results are available on the number of automorphisms of an automaton. For the class of cyclic automata the best result is Bavel's [1]: the number of automorphisms divides the number of generators of the automaton. For the class of non-cyclic automata the only result seems to be Feichtinger's [4], who gives an upperbound to the number of automorphisms of a non-cyclic automaton. In this note it will be shown that the number of automorphisms divides Feichtinger's bound, which generalizes Bavel's result to the class of non-cyclic automata.