Lecture Notes in Computer Science Volume 2996, 2004, pp 282-293

The Syntactic Graph of a Sofic Shift

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We define a new invariant for the conjugacy of irreducible sofic shifts. This invariant, that we call the syntactic graph of a sofic shift, is the directed acyclic graph of characteristic groups of the non null regular \(\mathcal{D}\)-classes of the syntactic semigroup of the shift.