论文标题
细胞自动机的图和花圈产物
Graph and wreath products of cellular automata
论文作者
论文摘要
我们证明，在可数的图形产品下，两侧全班的自动态组的亚组集合被关闭。我们介绍了没有$ a $ cancellation的集体行动的概念（对于Abelian Group $ a $），并表明，当$ a $是有限的Abelian组时，$ G $是一组蜂窝自动机，其动作没有$ a $ a $ cancellation，这是$ cancellation automphist of Automorphist of Automorphism of Automphism of Automphist of Automphist of Automphism of Automphism of Automphism of Automphism in automphist of Automphism in automphist of Automphism of Automphist的启动。我们表明，所有自由的Abelian群体和自由组都接受此类蜂窝自动机。在单方面，我们证明了这些结果的变体，并具有合理的字母爆炸。
We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under countable graph products. We introduce the notion of a group action without $A$-cancellation (for an abelian group $A$), and show that when $A$ is a finite abelian group and $G$ is a group of cellular automata whose action does not have $A$-cancellation, the wreath product $A \wr G$ embeds in the automorphism group of a full shift. We show that all free abelian groups and free groups admit such cellular automata actions. In the one-sided case, we prove variants of these results with reasonable alphabet blow-ups.
