Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces

2026-09-23

AI Summary

本文通过量化替代过程中的信息量并使用合适的并行计算模型，提供了一种判断多维符号动力系统是否为sofic系统的有效方法。

Abstract

In symbolic dynamics, the fixed-point construction from arXiv:0910.2415 defines shift spaces of finite type whose configurations embed infinite hierarchies of tilings. This article provides a "black box" abstraction of this method phrased in terms of substitutions and $S$-adic limit spaces operating over sequences of increasingly large alphabets. By quantifying the amount of information computed by the substitutions at each level, and using a suitable parallel model of computation, we provide a simple positive criterion of multidimensional soficity that generalizes classical examples from the literature.

Problem

• symbolic dynamics
• shift spaces
• soficity
• substitutions

Innovation

• substitutions
• S-adic limit spaces
• multidimensional soficity
• parallel model of computation