概率转换器的遍历性，两个自动机的串行连接

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2021-12-01 DOI:10.1515/dma-2021-0034

I. A. Kruglov

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引用次数: 0

摘要

摘要本文给出了自动机串行连接遍历性的充要条件，在该条件下，替换Mealy自动机的输出序列被馈送到无输出替换自动机的输入。结果表明，Mealy自动机的状态转移概率矩阵完全不可分解的条件为作为自动机串行连接的概率变换器的遍历性提供了一个充分条件。还证明了如果Mealy自动机的部分状态转移函数是可交换的，那么串行连接的遍历性条件与两个原始概率转换器的遍历性等价。

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Ergodicity of the probabilistic converter, a serial connection of two automata

Abstract The paper provides necessary and sufficient conditions for the the ergodicity of a serial connection of automata under which the output sequence of a substitution Mealy automaton is fed to the input of an output-free substitution automaton. It is shown that the condition of complete indecomposability of the state transition probability matrix of a Mealy automaton provides a sufficient condition for ergodicity of the probabilistic converter as a serial connection of automata. It is also shown that if the partial state transition functions of a Mealy automaton commute, then the condition of ergodicity of a serial connection is equivalent to that of both original probabilistic converters.

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.