Title: The Moore and the Myhill Property For Strongly Irreducible Subshifts Of Finite Type Over Group Sets,
Abstract: We prove the Moore and the Myhill property for strongly irreducible subshifts
over right amenable and finitely right generated left homogeneous spaces with
finite stabilisers. Both properties together mean that the global transition
function of each big-cellular automaton with finite set of states and finite
neighbourhood over such a subshift is surjective if and only if it is
pre-injective. This statement is known as Garden of Eden theorem.
Pre-Injectivity means that two global configurations that differ at most on a
finite subset and have the same image under the global transition function must
be identical.