加性细胞自动机的同构性分析

根据矩阵方程理论和细胞自动机原理，提出了加性细胞自动机状态转移结构的同构性方法，该方法利用状态转移矩阵方程及其特征多项式分析规则90和150加性细胞自动机，证明了特征多项式为不可约多项式时的零边界规则90和150加性细胞自动机与其对应的线性细胞自动机具有相同结构的状态转移图，即它们同构。研究表明：该方法对实际的伪随机序列产生、通信和测试等领域具有应用推广价值。
关 键 词 加性细胞自动机; 特征多项式; 状态转移图; 同构性

Abstract From the matrix theory and cellular automata theory, this paper presented the homogeneous characteristic methodology of cellular automata. The methodology utilized the state transition matrix equation and its characteristic polynomial to analyze the rule 90 and 150 additive cellular automata, and proved that if the characteristic polynomial of null boundary rule 90 and 150 linear cellular automata is non-dividable, then the states transition diagrams of the null boundary rule 90 and 150 additive cellular automata responding to the linear cellular automata have identical structure, while have different states. Research indicates that this methodology have advantages in the application fields of pseudorandom sequence generation, communications, and test.
Key words additive cellular automata; characteristic polynomial; state transition diagram; homogeneous characteristic