AI 中文总结
本文提出一种基于替换和$S$-adic极限空间的“黑盒”抽象，通过量化层级信息量并利用并行计算模型，给出多维sofic性的简单正判据，推广了经典例子。
AI 中文摘要
在符号动力学中，arXiv:0910.2415 中的不动点构造定义了有限型移位空间，其配置嵌入无限层级的平铺层次。本文将该方法抽象为一种“黑盒”表述，以替换和 $S$-adic 极限空间为框架，作用于字母表规模逐渐增大的序列之上。通过量化每个层级上替换所计算的信息量，并采用合适的并行计算模型，我们给出了一个简单的多维 sofic 性正判据，该判据推广了文献中的经典例子。
英文摘要
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.
Comments71 pages, 18 figures
