Graph and wreath products of cellular automata



: Salo, Ville

Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

: SINGAPORE

: 2024

: International Journal of Algebra and Computation

: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION

: INT J ALGEBR COMPUT

: 31

: 0218-1967

: 1793-6500

DOI: https://doi.org/10.1142/S0218196724500553

: https://doi.org/10.1142/S0218196724500553

: https://arxiv.org/abs/2012.10186


We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under countable graph products. We introduce the notion of a group action without A-cancellation (for an abelian group A), and show that when A is a finite abelian group and G is a group of cellular automata whose action does not have A-cancellation, the wreath product A (sic) G embeds in the automorphism group of a full shift. We show that all free abelian groups and free groups admit such cellular automata actions. In the one-sided case, we prove variants of these results with reasonable alphabet blow-ups.



Last updated on 2025-26-06 at 13:47