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：本文建立了经典伊甸园定理在满移位及可服从群空间上对非均匀元胞自动机的若干推广。特别地，我们的结果定量描述了非均匀元胞自动机的部分预单射性与其像大小之间的关系。此外，在强不可约有限型子移位上，针对多维元胞自动机还获得了一个加强的满射性结果。