Class-closing factor codes and constant-class-to-one factor codes from shifts of finite type

TL;DR

This paper introduces class-closing factor codes in shifts of finite type, explores their properties, and generalizes existing results on constant-class-to-one codes, establishing key relations among various types of factor codes.

Contribution

It defines class-closing factor codes, proves their continuation properties, and generalizes Nasu's result on constant-class-to-one codes between irreducible shifts of finite type.

Findings

Class-closing factor codes are continuing if their images are of finite type.

A factor code between irreducible shifts of finite type is constant-class-to-one iff it is bi-class-closing.

The paper establishes relations between class-closing, continuing, and constant-class-to-one factor codes.

Abstract

We define class-closing factor codes from shifts of finite type and show that they are continuing if their images are of finite type. We establish several relations between class-closing factor codes, continuing factor codes and constant-class-to-one factor codes. In particular it is shown that a factor code between irreducible shifts of finite type is constant-class-to-one if and only if it is bi-class-closing, generalizing a result of Nasu.