2025/10/16 by Castronuovo, Niccolo', Dennunzio, Alberto, Margara, Luciano
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.2510.14568
Group cellular automata are continuous, shift-commuting endomorphisms of G^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.