# On the Structure of Covers of Sofic Shifts

## TL;DR

This paper introduces a canonical cover for sofic shifts, analyzes their layered structures, and explores implications for flow invariants and C*-algebra ideals, advancing understanding of sofic shift dynamics.

## Contribution

It presents a new canonical cover for arbitrary sofic shifts and reveals layered structures of existing covers, enhancing the analysis of their invariants and algebraic properties.

## Key findings

- The left Krieger and past set covers can be divided into natural layers.
- The range of a flow-invariant is characterized.
- Insights into the ideal structure of associated C*-algebras are provided.

## Abstract

A canonical cover generalizing the left Fischer cover to arbitrary sofic shifts is introduced and used to prove that the left Krieger cover and the past set cover of a sofic shift can be divided into natural layers. These results are used to find the range of a flow-invariant and to investigate the ideal structure of the universal C*-algebra associated to a sofic shift space.