Proceedings of JAC 2010 Journées Automates Cellulaires
نویسندگان
چکیده
The Moore-Myhill Garden of Eden theorem asserts that a cellular automaton with finite alphabet over a free abelian group of rank 2 is surjective if and only if it is pre-injective. Here, pre-injectivity means that two configurations which coincide outside of a finite subset of the group must coincide everywhere if they have the same image under the cellular automaton. The Garden of Eden theorem has been extended to amenable groups by Ceccherini-Silberstein, Machi and Scarabotti and to cellular automata defined over strongly irreducible subshifts of finite type by Fiorenzi. I will discuss these extensions as well as linear versions jointly obtained with Ceccherini-Silberstein.
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