Equivalence Relations of Mealy Automata

Two independent equivalence relations are considered for Mealy automata. Simulation equivalence, on the one hand, arises from a new multi-step simulation concept under the constraint that the process of switching from one automaton to the other is reversible. Retiming equivalence, on the other hand, is the congruence induced by the so called sliding axiom in the monoidal category of automata. It is shown that these two equivalence relations coincide, and a characterization is given for simulation/retiming equivalence in terms of transition diagrams.