TL;DR
This paper introduces a canonical extension of the future cover for sofic shifts, highlighting cases where it is isomorphic and others where it extends beyond the original.
Contribution
It defines a canonical extension of the future cover for sofic shifts, providing a unified framework for understanding their structure.
Findings
The cover is canonical similar to the future cover.
In some cases, the cover is isomorphic to the future cover.
In other cases, it provides a genuine extension.
Abstract
The paper describes a cover of the future cover of a sofic shift which is canonical in the same way as the future cover itself. In some cases the cover is isomorphic to the future cover and in other it is a genuine extension.
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