论文标题
具有随机规则的一维蜂窝自动机的弱稳定性解决方案
Weakly robust periodic solutions of one-dimensional cellular automata with random rules
论文作者
论文摘要
我们研究了$ 2 $ - 尼克堡的一维蜂窝自动机，其中有大量$ n $的州和随机选择的规则。我们专注于具有弱强大的周期性解决方案（WRP）的规则。 WRP是表现出空间和时间周期性的全球配置，并至少具有固定的严格正速度进入任何环境。我们的主要结果量化了WRP的不可能：只要满足划分条件，就有有限的周期内WRP存在的可能性与$ 1/n $成正比。我们的主要工具来自随机图理论和用于泊松近似的陈斯坦方法。
We study $2$-neighbor one-dimensional cellular automata with a large number $n$ of states and randomly selected rules. We focus on the rules with weakly robust periodic solutions (WRPS). WRPS are global configurations that exhibit spatial and temporal periodicity and advance into any environment with at least a fixed strictly positive velocity. Our main result quantifies how unlikely WRPS are: the probability of existence of a WRPS within a finite range of periods is asymptotically proportional to $1/n$, provided that a divisibility condition is satisfied. Our main tools come from random graph theory and the Chen-Stein method for Poisson approximation.
