Year: 2024
Type: article
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 [Formula: see text] 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.
Author: Ville Salo
Institution: University of Turku
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403712546