Behavior of Finite Automata under Three Types of Responses of a Stationary Stochastic Medium

The article analyzes some cases of the behavior of finite automata in stationary stochastic media under three types of responses of the medium. The medium reacts to each action of the automata either by rewarding it, by penalizing it, or by being indifferent. It is shown that the purposefulness of the forms of behavior of finite automata depends on the structure of the medium. Conditions are obtained such that the choice of a given form of behavior (active or passive) is most purposeful. Asymptotic optimality of the automata in question is analyzed.