Gardens of Eden and amenability on cellular automata
Two new characterizations of amenable groups were yielded by proof a converse to the Garden-of-Eden theorem by Ceccherini-Silberstein, Machi and Scarabotti and to a theorem of \textit{T.~Meywrovitch} [``Finite entropy for multidimensional cellular automata'', Ergodic Theory Dynam. Systems 28, 1243--1260 (2008; Zbl 1152.37009)]. In particular, the following is proved to be equivalent: the group \(G\) is amenable, all cellular automata living on \(G\) that admit mutually erasable patterns also admit gardens of Eden; all cellular automata living on \(G\) that do not preserve Bernoulli measure admit gardens of Eden.
scientific article; zbMATH DE number 5663855
scientific article