The Myhill property for strongly irreducible subshifts over amenable groups

Tullio Ceccherini-Silberstein, Michel Coornaert

Published 2010-04-14, updated 2010-09-22Version 2

Let $G$ be an amenable group and let $A$ be a finite set. We prove that if $X \subset A^G$ is a strongly irreducible subshift then $X$ has the Myhill property, that is, every pre-injective cellular automaton $\tau \colon X \to X$ is surjective.