The Weyl pseudo-metric is a shift-invariant pseudo-metric over the set of infinite sequences, that enjoys interesting properties and is suitable for studying the dynamics of cellular automata. It corresponds to the asymptotic behavior of the Hamming distance on longer and longer subwords. In this paper we characterize well-defined dill maps (which are a generalization of cellular automata and substitutions) in the Weyl space and the sliding Feldman-Katok space where the Hamming distance appearing in the Weyl pseudo-metrics is replaced by the Levenshtein distance.

翻译：Weyl伪度量是定义在无限序列集合上的一种平移不变伪度量，具有许多有趣的性质，特别适用于研究元胞自动机的动力学行为。它对应于在越来越长的子词上汉明距离的渐近行为。本文刻画了在Weyl空间和滑动Feldman-Katok空间中良定义的扩张映射（这是元胞自动机和代换的推广），其中Weyl伪度量中出现的汉明距离被替换为莱文斯坦距离。