On the Structure of Covers of Sofic Shifts

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 $\Cs$-algebra associated to a sofic shift space.

2010 Mathematics Subject Classification: Primary: 37B10; Secondary: 46L05

Keywords and Phrases: shift space, sofic shift, Krieger cover, Fischer cover

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