The author defines a ”c-order semi-input memory finite automaton” and gives conditions under which it can be constructed, yielding bounded propagation of weakly decoding errors. As a corollary, it is shown that a finite automaton M is feedforward invertible with delay \(\tau\) if and only if there is a finite automaton M’, which is a weak inverse with delay \(\tau\) of M, such that propagation of decoding errors of M’ for M is bounded.