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首页> 外文期刊>Acta Ciencia Indica. Mathematics >FINITE AUTOMATA AND MARKOV PROCESS
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FINITE AUTOMATA AND MARKOV PROCESS

机译：有限自动和马尔可夫过程

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A Markov process is a stochastic system capable of assuming one of n-states s_1, s_2, ..., s_n and states change only at discrete points in time. The probability of transition from one state to other is defined as the transition probability p_(ij) with conditions 0 ≤ p_(ij) ≤ 1 and ∑p_(ij) =1. An n-state Markov process is an n-vertex, weighted, connected digraph G. The vertices of G correspond to the states and an edge (s_i, s_j) with a non-zero weight p_(ij) represent the non-zero transition probability from state s_i to s_j. Such a digraph is called transition graph, which has great importance in studying the Markov process. A digraph in which the edge weights are the sum of weights of edges emanating from a vertex is unity is called a stochastic graph. In many engineering problems, signal flow graphs can be constructed from a set of equations, directly without writing the equations. In this paper we convert the state transition function of finite state automata into a signal flow graph and discuss the steady state probability of the automata at any instant, using Markov process.
机译：马尔可夫过程是一种随机系统，能够假设n个状态s_1，s_2，...，s_n之一，并且状态仅在离散的时间点发生变化。从一种状态过渡到另一种状态的概率定义为条件0≤p_（ij）≤1和∑p_（ij）= 1的过渡概率p_（ij）。 n状态马尔可夫过程是n个顶点，加权的，连通的有向图G。G的顶点与状态相对应，权重p_（ij）为非零的边（s_i，s_j）表示非零跃迁。从状态s_i到s_j的概率。这样的图被称为过渡图，它在研究马尔可夫过程中非常重要。将边的权重是从顶点发出的边的权重之和为一的二阶图称为随机图。在许多工程问题中，可以直接由一组方程式构造信号流图，而无需编写方程式。在本文中，我们将有限状态自动机的状态转换函数转换为信号流图，并使用马尔可夫过程讨论自动机在任何时刻的稳态概率。

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