On the Period of a Periodic-Finite-Type Shift

TL;DR

This paper explores how the inherent period in periodic-finite-type shifts (PFTs) affects their properties and distinguishes them from shifts of finite type (SFTs), expanding understanding of sofic shifts.

Contribution

It provides a detailed analysis of the influence of the period on PFTs, clarifying their differences from SFTs and contributing to the theoretical understanding of sofic shifts.

Findings

Period significantly influences PFT properties

PFTs form a broader class than SFTs due to periodicity

The period affects the structural and dynamical characteristics

Abstract

Periodic-finite-type shifts (PFT's) form a class of sofic shifts that strictly contains the class of shifts of finite type (SFT's). In this paper, we investigate how the notion of "period" inherent in the definition of a PFT causes it to differ from an SFT, and how the period influences the properties of a PFT.