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.
翻译:我们建立了非均匀细胞自动机在全移动与可测群宇宙上的伊甸园定理的几个扩展。特别地,我们的结果定量地描述了非均匀细胞自动机的部分前射性和图像大小之间的关系。此外, 对于有限类型强不可约子移动的多维细胞自动机,我们也得到了强化的映射结果。