The Structures of Automata to Adapt to an Unknown Environment

A general fixed structure automaton acting in stationary random multireaction environment is described. Some necessary conditions are shown for automata to be purposeful or adaptive in an unknown environment (to be more profitable than a no-purpose, or random, automaton). By the necessary conditions it is proved that there exists no perfectly adaptive automaton. A necessary condition for automata with minimum state space to be purposeful is obtained. This condition characterizes their structures explicitly, so that a little restriction gives a sufficient condition. Some general subclasses of automata are proposed, and necessary and sufficient conditions for such automata to be purposeful are investigated. Furthermore as properties of a purposeful automaton, the time required to adapt and the stability of adapting to the random environment are discussed.