论文标题
一些关于换档空间分类的注释：有限类型的变化； SOFIC转移；和有限定义的班次
Some notes on the classification of shift spaces: Shifts of Finite Type; Sofic Shifts; and Finitely Defined Shifts
论文作者
论文摘要
本文的目的是找到适当的定义，以在符号动态的一般环境中有限类型和SOFIC转移的变化。我们开始表明，有限类型和SOFIC偏移的经典定义是在有限的alphabet偏移空间上给出的，在一维单型$ \ mathbb {n} $或$ \ \ \ \ m mathbb {z} $的情况下，它们与通常的金额不适合过度的无限alpheTobet或其他单元。因此，通过检查有限类型和SOFIC变化的经典定义中的核心特征，我们提出了可以在任何情况下使用的一般定义。有限类型的换档的替代定义激发了新的一类移动空间的定义，该空间与Sofic Shift类别相交，并包括有限类型的偏移。该新类被命名为有限定义的偏移，其非限制型换档被命名为可变长度的变化。对于晶格$ \ mathbb {n} $或$ \ mathbb {z} $的特定情况，使用通常的总和，可变长度的偏移可以解释为可变长度长度马尔可夫链的拓扑版本。
The aim of this article is to find appropriate definitions for shifts of finite type and sofic shifts in a general context of symbolic dynamics. We start showing that the classical definitions of shifts of finite type and sofic shifts, as they are given in the context of finite-alphabet shift spaces on the one-dimensional monoid $\mathbb{N}$ or $\mathbb{Z}$ with the usual sum, do not fit for shift spaces over infinite alphabet or on other monoids. Therefore, by examining the core features in the classical definitions of shifts of finite type and sofic shifts, we propose general definitions that can be used in any context. The alternative definition given for shifts of finite type inspires the definition of a new class of shift spaces which intersects with the class of sofic shifts and includes shifts of finite type. This new class is named finitely defined shifts, and the non-finite-type shifts in it are named shifts of variable length. For the specific case of infinite-alphabet shifts on the lattice $\mathbb{N}$ or $\mathbb{Z}$ with the usual sum, shifts of variable length can be interpreted as the topological version of variable length Markov chains.
