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We consider Additive CA on a finite group, also called Group CA. First of all, we present the abelian situation in which easy-to-check algebraic characterizations of the main dynamical properties in terms of the CA local rule have been provided. Then, we move to the non abelian scenario. Precisely, we consider the dynamical behavior of Additive CA on a number of classes of specific finite groups and for each of those classes, we focus our attention to the non abelian scenarios, providing exact characterizations for some dynamical properties.

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Toward Non Abelian Scenarios for Additive Cellular Automata on Finite Groups

  • 会议论文

  • 发表日期：

    2026年

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  • Alberto Dennunzio

摘要

We consider Additive CA on a finite group, also called Group CA. First of all, we present the abelian situation in which easy-to-check algebraic characterizations of the main dynamical properties in terms of the CA local rule have been provided. Then, we move to the non abelian scenario. Precisely, we consider the dynamical behavior of Additive CA on a number of classes of specific finite groups and for each of those classes, we focus our attention to the non abelian scenarios, providing exact characterizations for some dynamical properties.