A1 Refereed original research article in a scientific journal
Graph and wreath products of cellular automata
Authors: Salo, Ville
Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
Publishing place: SINGAPORE
Publication year: 2024
Journal: International Journal of Algebra and Computation
Journal name in source: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Journal acronym: INT J ALGEBR COMPUT
Number of pages: 31
ISSN: 0218-1967
eISSN: 1793-6500
DOI: https://doi.org/10.1142/S0218196724500553
Web address : https://doi.org/10.1142/S0218196724500553
Abstract
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.
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.
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