Abstract
We define a class of factor maps between sofic shifts, called lifting maps, which generalize the closing maps. We show that an irreducible sofic shiftS has only finitely manyS-conjugacy classes of minimal left (or right) lifting covers. The number of these classes is a computable conjugacy invariant ofS. Furthermore, every left lifting cover factors through a minimal left lifting cover.
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Trow, P. Lifting covers of sofic shifts. Monatshefte für Mathematik 125, 327–342 (1998). https://doi.org/10.1007/BF01305347
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DOI: https://doi.org/10.1007/BF01305347