Amenable groups and cellular automata
Tullio G. Ceccherini-Silberstein, Antonio Machı̀, Fabio Scarabotti · Annales de l’institut Fourier · 1999
We show that the theorems of Moore and Myhill hold for cellular automata whose universes are Cayley graphs of amenable finitely generated groups. This extends the analogous result of A. Machi and F. Mignosi “Garden of Eden configurations for cellular automata on Cayley graphs of groups” for groups of sub-exponential growth.