Flow equivalence of sofic shifts

TL;DR

This paper classifies a specific class of sofic shifts called PET shifts up to flow equivalence by using invariants derived from their Fischer covers, extending previous classification methods.

Contribution

It introduces an extension theorem for flow equivalences and classifies PET sofic shifts using algebraic invariants of associated G-SFTs, advancing the understanding of flow equivalence.

Findings

Classification of PET sofic shifts up to flow equivalence

Development of an extension theorem for flow equivalences

Use of algebraic invariants of G-SFTs for classification

Abstract

We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients: (1) An extension theorem, for extending flow equivalences of subshifts to flow equivalent irreducible shifts of finite type which contain them. (2) The classification of certain constant to one maps from SFTs via algebraic invariants of associated G-SFTs.