中文摘要：

本文刻画了输入存贮线性有限自动机本身结构矩阵的特点，证明了两个输入存贮线性有限自动机作积（后并、全直积、化合）之后仍然是输入存贮线性有限自动机，给出了两个输入存贮线性有限自动机作积之后的结构矩阵、自由响应生成矩阵、传输函数矩阵和原来两个输入存贮线性有限自动机的结构矩阵、自由响应生成矩阵、传输函数矩阵的关系。得出线性有限自动机M具有r阶输入存贮的等价命题。

英文摘要：

The structure matrix of an input-memory linear finite automaton is characterized in this paper. It is proved that the full direct product, back connection and composition of two input-memory linear finite automata are still input-memory linear finite automata. The structure matrix, free response matrix and transfer function matrix of the full direct product, back connection and composition of two input-memory linear finite automata are constructed by using the corresponding matrices of the original two input-memory linear finite automata, respectively. An equivalent characterization for a liner finite automaton to be r-order input-memory is given.