We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts Sβ. We show that any reversible CA F:Sβ → Sβ has an almost equicontinuous direction whenever Sβ is not sofic. This has the corollary that non-sofic beta-shifts are topologically direct prime, i.e. they are not conjugate to direct topological factorizations X × Y of two nontrivial subshifts X and Y. We also make some preliminary observations on direct topological factorizations of beta-shifts that are subshifts of finite type.
CITATION STYLE
Kopra, J. (2020). Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12086 LNCS, pp. 178–191). Springer. https://doi.org/10.1007/978-3-030-48516-0_14
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