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93 is homogeneous arbitrary automata theory automaton 21 automaton covering called Card Card(Z closure operations Comp Consequently constructed Corollary Definition denote deterministic automaton elementary event equivalence classes equivalence relation equivalently embedded fc-stable finite automata finite number Furthermore hence homogeneous with respect IEEE IEEE Trans implies induction step Information and Control initial automaton initial step input alphabet input signals Lemma maton Moore automaton ND-automaton 93 ND-Mealy automaton non-deterministic number of steps obtain Obviously output signal partial automaton partition probabilistic automata Proof Proposition random regular expressions regular term represented S-Mealy S-operator satisfied sequence sequential circuits sequential machines sequential ND-operator set of words single-valued mapping singleton standard term stochastic automata stochastic event strongly reduced Suppose terminal equivalent terminal minimal terminal reduced Theorem trivial Val(T weakly equivalent weakly initial weakly k-stable word function Z-finite S-automaton Z-homomorphism Z-isomorphic