标题： Avoshifts、Unishifts和非确定性细胞自动机 显示英文标题

标题： Avoshifts, Unishifts and Nondeterministic Cellular Automata

摘要： 本文研究了$\mathbb{Z}^d$上的 avoshift 和 unishift。avoshift 是一类子移位，对于任意凸集$C$和向量$v$（使得$C \cup \{\vec v\}$也是凸的），全局有效模式在$C$上的合法扩展到$C \cup \{v\}$上的集合由$C$的有界子模式确定。 单向移位（unishifts）是这样的子移位：对于某个给定的 $C, \vec v$，每个 $C$-模式具有相同数量的 $\vec v$-扩展。单元格式拟群移位（包括群移位）和 TEP 子移位是单向移位的例子，而单向移位以及具有拓扑强空间混合的子移位是 ava 移位（avoshifts）的例子。 我们证明了每个 ava 移位都是低维 ava 移位上一个非确定性细胞自动机的空间时间子移位，这可以通过线性变换和凸阻塞实现。由此得出结论，所有 ava 移位都包含周期点，并且单向移位具有稠密的周期点并且允许等熵的完全移位因子。 显示英文摘要

摘要： In this paper, we study avoshifts and unishifts on $\mathbb{Z}^d$. Avoshifts are subshifts where for each convex set $C$, and each vector $v$ such that $C \cup \{\vec v\}$ is also convex, the set of valid extensions of globally valid patterns on $C$ to ones on $C \cup \{v\}$ is determined by a bounded subpattern of $C$. Unishifts are the subshifts where for such $C, \vec v$, every $C$-pattern has the same number of $\vec v$-extensions. Cellwise quasigroup shifts (including group shifts) and TEP subshifts are examples of unishifts, while unishifts and subshifts with topological strong spatial mixing are examples of avoshifts. We prove that every avoshift is the spacetime subshift of a nondeterministic cellular automaton on an avoshift of lower dimension up to a linear transformation and a convex blocking. From this, we deduce that all avoshifts contain periodic points, and that unishifts have dense periodic points and admit equal entropy full shift factors.