  Antonenko and Russyev independently have shown that any Mealy automaton with
no cycles with exit--that is, where every cycle in the underlying directed
graph is a sink component--generates a fi- nite (semi)group, regardless of the
choice of the production functions. Antonenko has proved that this constitutes
a characterization in the non-invertible case and asked for the invertible
case, which is proved in this paper.
