Realization of the one statistical rule for automation

Finite automatons are the most convenient objects for constructing mathematical models of complex systems. The role of simple objects in such systems can be considered as finite automatons for both deterministic and probabilistic (stochastic) structures. In the stationary random environment, the task of the automaton is special interest in the automatons that the behavior of which is advisable and the structure of which does not have any information about the functionality of the stationary environment. The structure of such automaton should ensure the symmetry: In case of different actions by the automaton, the automaton's behavior should be identical if series of signals on the entrance of the automaton are same. The problem of automaton conducting in the stationary random environment, as in the case of nondeterministic, the task of choosing the best of any criterion, was formulated and developed by Tsetlin [1]. In the simplest case, environment reactions to the automaton actions are: either "reward" or "fine" the automaton. The automaton on the environment does not have prior information. Automaton behavior in such an environment is considered advisable if the average profit of the automaton exceeds the gain of a automaton that chooses to act independently from the environmental reactions and equally. However, as research by various authors has shown (see, for example, [2-5]), such a automaton can be better than any criterion in any environment. Consequently, it is important to build a wide range of automaton-building structures and develop analytical and numerical methods to calculate the basic statistical characteristics of their behavior that can be used to solve various practical problems. In the master's thesis, a series of well-known statistical rules from the theory of recuperative sequences: "m series of successes, or l series of failures" are based on three possible reactions (win, loss, indifference) in stationary random constructions of finite automatons (algorithms of behavior). The methods of the random walk theory have been adopted by the formulas for the possibilities of the probability of changing the action of the engines which are calculated by the basic statistical characteristics of the automaton's behavior. It is also shown that the sequence of the construction of the constructed structures is bound to the infinite structure of the same structure, and is researched and analyzed. Automaton experiments have been conducted on these issues. The graphs of the obtained results are presented and the relevant analysis has been conducted.

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