Ergodicity, transitivity, and regularity for linear cellular automata over Zm

被引：34
|
作者：
Cattaneo, G
Formenti, E
Manzini, G
Margara, L
机构：
[1] Univ Milan, Dipartimento Sci Informaz, I-20135 Milan, Italy
[2] Univ Turin, Dipart Sci & Tecnol Avanzante, Turin, Italy
[3] Univ Bologna, Dipartimento Sci Informaz, I-40127 Bologna, Italy
来源：
THEORETICAL COMPUTER SCIENCE | 2000年 / 233卷 / 1-2期
关键词：
discrete time dynamical systems; cellular automata; ergodicity; topological transitivity;
D O I：
10.1016/S0304-3975(98)00005-X
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We study the dynamical behavior of D-dimensional linear cellular automata over Z(m). We provide an easy-to-check necessary and sufficient condition for a D-dimensional linear cellular automata over Z(m) to be ergodic and topologically transitive. As a byproduct, we get that for linear cellular automata ergodicity is equivalent to topological transitivity. Finally, we prove that for 1-dimensional linear cellular automata over Z(m), regularity (denseness of periodic orbits) is equivalent to surjectivity. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：147 / 164
页数：18
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