The Garden of Eden Theorem for Cellular Automata on Group Sets
نویسنده
چکیده
We prove the Garden of Eden theorem for cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It states that the global transition function of such an automaton is surjective if and only if it is preinjective. 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.
منابع مشابه
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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...
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