On the Garden of Eden theorem for non-uniform cellular automata

04/03/2023

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by   Xuan Kien Phung, et al.

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We establish several extensions of the well-known Garden of Eden theorem for non-uniform cellular automata over the full shifts and over amenable group universes. In particular, our results describe quantitatively the relations between the partial pre-injectivity and the size of the image of a non-uniform cellular automata. A strengthened surjunctivity result is also obtained for multi-dimensional cellular automata over strongly irreducible subshifts of finite type.