Reconstruction of the Initial State Vector of Nonlinear Automata over a Finite Ring

Abstract

For Mealy and Moore automata over a finite commutative-associative ring with unity, which transition function is defined by nonlinear equations of the second degree, and the output function is affine and linear map of the states set, respectively, the problem of reconstruction of the initial state vector is solved. The case, when this problem is trivial, is considered. It is found that in other cases the problem is difficult. It is found that the property "to be reversible automaton" generally does not affect the complexity of solving the problem of reconstruction of the initial state vector for the investigated automata.