SOME RESULTS ON THE STRUCTURE OF FEEDFORWARD INVERSES
Ran Tao · 1984
Let M'=@(M_a,f) be a semi-input-memory finite automaton with input alphabet Y andoutput alphabet X. In this paper, the following results are given: (i) If #X = #Y, then M'is a feedforward inverse with delay free if and only if there exists a cycle C of the statediagram of M_a such that #f (y_0,…, y_(c-1), Y, λ(P)) = #X for any state p in C and y_0, …,y_(c-1) in Y. (ii) If X = Y = {0, 1}, then M' is a feedforward inverse with delay 1 if and onlyif there exists a cycle C of state diagram of M_a such that f(y_0, …,y_c,λ_a(p)) can be expressedin the form of f'(y_0,…,y_(c-1),λ_a(p)) ?y_c for any state p in C and y_0,…,y_c in Y, or of f(y_0,…,y_(c-2),λ_a(p))?y_(c-1) for any state p in C and y_0,…,y_c in Y.