Algorithms for computing the sets of stochastic matrices with predefined properties, based on automaton models

Abstract

The formed sets of ergodic stochastic matrices are focused on solving the problem of classifying probabilistic automaton models by certain criteria/parameters of similarities or differences in the structures of ergodic stochastic matrices using the methods of applied multivariate mathematical statistics. The algorithms developed allow forming a variety of the sets of stochastic matrices through changing the transition and random entry function in a probabilistic automaton. Transition function of the autonomous probabilistic automaton allows using the probabilistic automaton operation algorithm proposed to form the sets of ergodic stochastic matrices that differ in their potencies and structures, based on implementing state set permutations with repetitions and changing the random input variable probability distributions. Defining various autonomous deterministic automaton output functions, we can use the algorithm developed to form the sets of ergodic stochastic matrices that differ in their potencies, with a specified limiting vector, based on implementing the permutations of a set of output letters with repetitions. We are also presenting the evaluations of the potencies of the sets of ergodic stochastic matrices with rational elements, represented by autonomous probabilistic automata under the given constraints.