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On the Garden of Eden theorem for non-uniform cellular automata (2304.00661v1)
Published 3 Apr 2023 in math.DS, cs.DM, math-ph, math.MP, and nlin.CG
Abstract: 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.