A conjugacy invariant for reducible sofic shifts and its semigroup characterizations |
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Authors: | Nataša Jonoska |
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Institution: | (1) Department of Mathematics, University of South Florida, 33620-5700 Tampa, FL, USA |
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Abstract: | We introduce a notion of magic words and, through them, we present a lattice of sub-synchronizing subshifts which describes
the synchronizing parts of a sofic shiftS. We show that topological conjugacy maps subsynchronizing subshifts onto sub-synchronizing subshifts, it preserves their
mutual relationship (i.e. the corresponding lattices are isomorphic) and the corresponding covers within the Krieger covers
are topologically conjugate. Using the magic words, a full characterization of the syntactic monoid of a shift of finite type
is given. We show that a synchronizing deterministic presentation of every sub-synchronizing subshift ofS can be seen within a two-sided ideal of the syntactic monoid ofS. |
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Keywords: | |
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