Abstract
The purpose of this paper is to consider the behavior of a finite automaton in a nonstationary random environment. The behavior of finite deterministic automata in stationary random environments was considered by Tsetlin. In this paper, the probabilistic automaton is introduced as a random environment in order to generalize the stationary random environment. The interaction between the probabilistic automaton and the two-state deterministic automaton is considered in the case where the probabilistic automaton has two inputs and two states and, besides, is completely isolated by the 0th approximation. And the limiting state probability distribution of this finite automaton is also obtained. Moreover, it is shown that, if the probabilistic automaton is completely isolated by the (0, k)th approximation and satisfies some conditions, then the finite automaton can behave expediently against the probabilistic automaton.
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