Indistinguishability of finite automata in a stationary observation environment

We find criteria for the finiteness of classes of automata that are indistinguishable by simple experiments of unlimited and fixed length under the condition that, instead of an input-output sequence generated by an automaton, the experimenter observes the result of its coding by some discrete function (the observation environment). Under these same observation conditions we obtain a criterion for the chain condition of classes of automata that are indistinguishable by experiments of fixed length, with an increase in the length of the experiment.