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arXiv · 2510.14568

Decidability and Characterization of Expansivity for Group Cellular Automata

Niccolo' Castronuovo·Alberto Dennunzio·Luciano Margara
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Abstract

Group cellular automata are continuous, shift-commuting endomorphisms of $G^\mathbb{Z}$, where $G$ is a finite group. We provide an easy-to-check characterization of expansivity for group cellular automata on abelian groups and we prove that expansivity is a decidable property for general (non-abelian) groups. Moreover, we show that the class of expansive group cellular automata is strictly contained in that of topologically transitive injective group cellular automata.

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Niccolo' Castronuovo, Alberto Dennunzio, Luciano Margara. 2025-10-16. Decidability and Characterization of Expansivity for Group Cellular Automata. https://arxiv.org/abs/2510.14568

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