Constructing finite automata with invertibility by transformation method

Ra,Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In a previous paper, the authors generalizedRa,Rb transformations to deal with nonlinear memory finite automata, and gave sufficient conditions for weak inverse and for weakly invertible memory finite automata and inversion processes concerned; methods by transformation to generate a kind of nonlinear memory finite automata satisfying one of these sufficient conditions were also given. This paper extends the concepts, methods and results to general finite automata, in which states consist of finite input history, finite output history and finite “inner state” history.