整数格上随机布尔元胞自动机的稳定性
Stability in random Boolean cellular automata on the integer lattice
摘要：
我们考虑整数格上的随机布尔元胞自动机，即，用从1到$N$的整数标识小区。自动机的行为主要取决于随机变量的支持度，该随机变量为每个单元格独立地选择16个可能的布尔规则之一。如果一个细胞在一段时间后不再改变其状态，则称其稳定。我们根据随机布尔自动机的稳定概率的正性对其进行分类。这里是一个例子的结果，我们的结果：如果支持包含至少5个规则，然后渐近$N$趋于无穷的概率稳定是积极的，而存在随机布尔元胞自动机与4个规则，在他们的支持，这个概率趋于0。
英文摘要：
We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one of the sixteen possible Boolean rules, independently for each cell. A cell is said to stabilize if it will not change its state anymore after some time. We classify the random boolean automata according to the positivity of their probability of stabilization. Here is an example of a consequence of our results: if the support contains at least 5 rules, then asymptotically as $N$ tends to infinity the probability of stabilization is positive, whereas there exist random boolean cellular automata with 4 rules in their support for which this probability tends to 0.
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