On half-synchronized systems

TL;DR

This paper studies half-synchronized systems, a subclass of coded systems, demonstrating their properties under hyperbolic maps and establishing an equivalence relation, with implications for factor maps and decoding.

Contribution

It introduces the concept of half-synchronized systems, shows their properties under hyperbolic maps, and explores their role in factor maps and decoding.

Findings

Half-synchronized systems are closed under hyperbolic maps.

An equivalence relation is established on half-synchronized systems.

Right-closing a.e., 1-1 a.e. factor maps have strong decoding properties when the domain is half-synchronized.

Abstract

A subclass of coded systems containing synchronized systems is the family of half-synchronized systems. In this note, we will consider them and show that the property half-synchronized lifts under hyperbolic maps. This enables us to define an equivalence relation on the set of half-synchronized systems. Also, when the domain is half-synchronized, we show that right-closing a.e., 1-1 a.e. factor maps have a strong decoding property.