关于概率自动机的分解

ANALYSIS OF PROBABILISTIC AUTOMATA

在[1]中给出了有穷状态概率自动机A(BA A)可以分解为随机编码源T与确定型自动机B(DA B)的顺次连结,并用例子说明了分解的算法。该结论及算法是建立在随机向量的蕴含与随机矩陈凸分解的基础上。由于BA A的转移矩阵A(y/x)一般不是随机矩阵,因而[1]中首先由A(y/x)构造出相应的随机矩阵A(x)与C(x)才能进行分解。本文是在推广了[1]中有关概念及结论的基础上给出了一个不依赖于随机矩阵的分解方法。本文所引用的符号与概念可参考[1]与[2]。

In [1], it shows that a probabilistic automata can be expressed in a codes source with a deterministic automata. However, the conclusion and its algoritim are given on the basis of the concepts of the implication of stochastic vecLors and convex analysis of stochastic matrix. And the transition matrix usually is not stochastic matrix. We, therefore, have to form the corresponding stochastic matrixes with transition matrixes. In this way, we can resolve them into the simple marries, This paper has expressed the corresponding concepts and the conclusions in [1]. On the basis of the concepts and the conclusion, it points out that an analysis algorithm dose not depend on stochastic matrixes.