caa a22 4500 378896776 CHVBK 20180305123508.0 cr unu---uuuuu 161128e20040701xx s 000 0 eng 10.1515/1569392031905575 doi (NATIONALLICENCE)gruyter-10.1515/1569392031905575 Nurutdinov Sh. R. Implementation of Markov chains over Galois fields [Elektronische Daten] [Sh. R. Nurutdinov] The automaton implementation of a determinate function is a probabilistic automaton A 1 = (S, Y, P s, λ(s)), where S is the Markov chain state set, Ps is an m 1 × m 1 stochastic matrix, Y is the output alphabet of cardinality m 2 ≤ m 1. The automaton implementation of a probabilistic function is a probabilistic automaton A 2 = (S, Y, Ps, Py ), where S, Y, Ps are of the same sense as in A 1, while Py is a stochastic m 1 × m 2 matrix. In this paper, we solve the problem of synthesis of generators of finite homogeneous Markov chains on the base of the analytical apparatus of polynomial functions over a Galois field. We suggest a method to calculate the coefficients of a polynomial in several variables which implements any mapping of the Galois field into itself. We study the case of implementing a finite automaton by a homogeneous computing structure defined over a Galois field; automaton mappings are implemented as polynomial functions over the Galois field. As the base polynomials, we use polynomial functions over the Galois field. As the base polynomials, we use polynomial functions over the Galois field where r = 2 n - 1, x, s, bi, aij ∈ GF(2 n ). We give expressions of an automaton A 1 in the framework of a polynomial model over the field GF(2 n ) of the form M 1 = (, f 1(x, s), f 2(s)), where is the discrete random variable which takes values µ ∈ GF(2 n ) determined by some probability vector = (p 1, . . . , pk 1 ) such that where Bi are stochastic Boolean matrices and k 1 ≥ - m 1 + 1, and of an automaton M 2 = (, f 1(x, s), f 2(s), , f 3(x, s)), where is a discrete random variable which takes values µ′ ∈ GF(2 n ) determined by some probability vector = (p 1, . . . , pk 2) such that where Bi are stochastic Boolean matrices and k 2 ≥ - m 1 + 1. The problem of representation of a discrete random variable over the field GF(2 n ) has been solved earlier. Copyright 2004, Walter de Gruyter Discrete Mathematics and Applications Walter de Gruyter 14/3(2004-07-01), 273-285 0924-9265 14:3<273 2004 14 dma https://doi.org/10.1515/1569392031905575 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569392031905575 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Nurutdinov Sh. R. NATIONALLICENCE 773 0- Discrete Mathematics and Applications Walter de Gruyter 14/3(2004-07-01), 273-285 0924-9265 14:3<273 2004 14 dma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter