GF(2^p)위에서의 SACA와 HCA의 특성에 관한 연구

Abstract

Cellular Automata(CA) has been used as modeling and computing paradigm for a long time. And CA has been used to model many physical systems. While studying the models of such systems, it is seen that as the complexity of the physical system increase, the CA based model becomes very complex and becomes to difficult to track analytically. A new cellular structure called GF(2^(p)) CA is analytically characterized in this thesis. Each cell of the GF(2^(p)) CA is capable of storing a value from the set {0,1,‥,2^(p)-1}. Though GF(2^(p)) CA can only handle data with bit units GF(2^(p)) HCA can handle data with units more than bit units. In this thesis we analyze the state­transition of nongroup CA with a single attractor over GF(2^(p)) and give the method for the construction of the state­transition diagram of a linear SACA over GF(2^(p)) by using the concept of basic path. And we propose the state­transition diagram of the nonlinear complemented SACA by using the state­transition diagram of a linear SACA. Also we analyze transition rules, characteristic polynomials and cyclic structures of HCA over GF(2^(p)).