On the asymptotic properties of a class stochastic finite automaton in a ternary stationary random medium

Author: Tariel Khvedelidze
Keywords: finite automaton, stationary random medium, behavior algorithm, the Markov chain, eigenvalue.
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Is proposed an algorithm the behavior of one class of a finite stochastic automaton in a stationary random medium with three possible reactions (win, loss, indifference). Is studied of eigenvalues Markov chain which describes behavior of a system in this medium. Is proved uniqueness eigenvalues of the tending modulo to 1 with increasing number of automaton memory and is estimated the rate of convergence.