标题： 关于非均匀细胞自动机的满射性和花园之梦定理 显示英文标题

标题： On the surjunctivity and the Garden of Eden theorem for non-uniform cellular automata

摘要： 非均匀细胞自动机（NUCA）是细胞自动机的一种扩展，在不同的单元格中具有多个局部规则。 我们证明，如果局部规则的分布是均匀遍历的，或者在一维情况下是遍历的，那么“伊甸园定理”成立。 我们还证明，对于任何非遍历的分布，存在一个局部规则的替换，该替换定义了一个不满足“伊甸园定理”的NUCA。 最后，我们证明，渐近于遍历分布的规则分布定义了一个双射的NUCA。 显示英文摘要

摘要： Non-uniform cellular automata (NUCA) are an extension of cellular automata with multiple local rules in different cells. We show that if the distribution of local rules is uniformly recurrent, or recurrent in the one-dimensional case, the Garden of Eden theorem holds. We also show that for any non-recurrent distribution, there is a substitution of local rules that defines a NUCA which does not satisfy the Garden of Eden theorem. Finally, we show that a rule distribution asymptotic to recurrent distribution defines a surjunctive NUCA.