根據矩陣方程理論和細胞自動機原理，提出了加性細胞自動機狀態(tài)轉移結構的同構性方法，該方法利用狀態(tài)轉移矩陣方程及其特征多項式分析規(guī)則90和150加性細胞自動機，證明了特征多項式為不可約多項式時的零邊界規(guī)則90和150加性細胞自動機與其對應的線性細胞自動機具有相同結構的狀態(tài)轉移圖，即它們同構。研究表明：該方法對實際的偽隨機序列產生、通信和測試等領域具有應用推廣價值。
關 鍵 詞 加性細胞自動機; 特征多項式; 狀態(tài)轉移圖; 同構性

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