标题： (非)同步性对ECA的影响：迈向新的分类 显示英文标题

标题： Impact of (a)Synchronism on ECA: Towards a New Classification

摘要： 本文研究了（非）同步性对初等细胞自动机动力学的影响。在我们的研究框架内，我们选择了五种不同的更新方案，这些方案是从周期性更新模式家族中选取的：并行、序列、块序列、块并行和局部时钟。我们主要的复杂性度量标准是每个规则动力学中极限环的最大周期。在此背景下，我们提出了ECA规则景观的分类。我们将大多数初等规则分为三个不同的类别：常数、线性和超多项式。令人惊讶的是，虽然一些规则在更广泛的更新方案下表现出更为复杂的动态行为，但其他规则在所有考虑的更新方案下表现出相似的行为。尽管我们能够在大多数情况下推导出极限环最大周期的上下限，但对某些规则的分析仍然开放。为了补充对88个初等规则的研究，我们引入了一个基于两个主要测量指标的数值模拟框架：配置的能量和密度。在此背景下，我们观察到一些规则根据更新方案显示出显著的变化，而另一些规则则保持稳定，这证实了理论分析所得分类的结果。 显示英文摘要

摘要： In this paper, we study the effect of (a)synchronism on the dynamics of elementary cellular automata. Within the framework of our study, we choose five distinct update schemes, selected from the family of periodic update modes: parallel, sequential, block-sequential, block-parallel, and local clocks. Our main measure of complexity is the maximum period of the limit cycles in the dynamics of each rule. In this context, we present a classification of the ECA rule landscape. We classified most elementary rules into three distinct regimes: constant, linear, and superpolynomial. Surprisingly, while some rules exhibit more complex behavior under a broader class of update schemes, others show similar behavior across all the considered update schemes. Although we are able to derive upper and lower bounds for the maximum period of the limit cycles in most cases, the analysis of some rules remains open. To complement the study of the 88 elementary rules, we introduce a numerical simulation framework based on two main measurements: the energy and density of the configurations. In this context, we observe that some rules exhibit significant variability depending on the update scheme, while others remain stable, confirming what was observed as a result of the classification obtained in the theoretical analysis.