The recognition of the output function of a finite automaton with random input

The output function recognition of a binary automaton with random Bernoulli input by the character frequency in the output sequence is considered. On the set of output functions, an equivalence relation is introduced, the classes of which consist of functions that are indistinguishable in the scheme. The problem of recognizing the equivalence class of the output function is reduced to the integer optimization problem. Three partial classes of automata close to shift registers are considered. © Springer Nature Switzerland AG 2018.