This work is a thoughtful extension of the ideas sketched in Montalva et al. (AUTOMATA 2017 exploratory papers proceedings, 2017), aiming at classifying elementary cellular automata (ECA) according to their maximal one-step sensitivity to changes in the schedule of cells update. It provides a complete classification of the ECA rule space for all period sizes \(n > 9\) and, together with the classification for all period sizes \(n \le 9\) presented in Montalva et al. (Chaos Solitons Fractals 113:209–220, 2018), closes this problem and opens further questionings. Most of the 256 ECA rule’s sensitivity is proved or disproved to be maximum thanks to an automatic application of basic methods. We formalize meticulous case disjunctions that lead to the results, and patch failing cases for some rules with simple arguments. This gives new insights on the dynamics of ECA rules depending on the proof method employed, as for the last rules 45 and 105 requiring \(({\texttt{0011}})^*\) induction patterns.

中文翻译：

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通过定期配置更新基本细胞自动机计划的最大灵敏度

这项工作是对蒙塔尔瓦（Montalva）等人所勾勒出的思想的深思熟虑的延伸。（AUTOMATA 2017探索性论文集，2017），旨在根据基本细胞自动机（ECA）对细胞更新时间表变化的最大单步敏感性进行分类。它为所有周期大小\（n> 9 \）提供ECA规则空间的完整分类，并为所有周期大小\（n \ le 9 \）提供分类在Montalva等人中提出。（Chaos Solitons Fractals 113：209–220，2018年），解决了这个问题并提出了进一步的质疑。由于自动应用了基本方法，因此256条ECA规则的灵敏度中的大多数已被证明或被否决。我们将导致结果的细致的个案析取形式化，并为带有简单参数的某些规则修补失败的个案。这取决于所采用的证明方法，为ECA规则的动态性提供了新的见解，至于最后的规则45和105需要\（（{\ texttt {0011}}）^ * \）归纳模式。