Emergent Mind
Graph and wreath products of cellular automata
(2012.10186)
Published Dec 18, 2020
in
math.GR
,
cs.FL
,
and
math.DS
Abstract
We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under graph products. We introduce the notion of an Aithful group action, and show that when A is a finite abelian group and G is a group of cellular automata whose action is Aithful, the wreath product A \wr G embeds in the automorphism group of a full shift. We show that all free abelian groups and free groups admit Aithful cellular automata actions. In the one-sided case, we prove variants of these result with reasonable alphabet blow-ups.
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