Dill maps in the Weyl-like space associated to the Levenshtein distance

TL;DR

This paper characterizes dill maps, a generalization of cellular automata, within Weyl and sliding Feldman-Katok spaces using the Levenshtein distance, extending the study of dynamics in these metric spaces.

Contribution

It introduces a characterization of dill maps in Weyl and Feldman-Katok spaces with Levenshtein distance, expanding the understanding of their dynamics.

Findings

Characterization of dill maps in Weyl space with Levenshtein distance

Extension of Weyl pseudo-metric properties to Levenshtein distance

Analysis of dynamical behavior of dill maps in new metric spaces

Abstract

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.