The Equivalence of Finite Valued Transducers (on HDTOL Languages) is Decidable

We show a generalization of the Ehrenfeucht Conjecture: For every language there exists a (finite) test set with respect to normalized k-valued finite transducers with bounded number of states. Further, we show that for each HDTOL language such a test set can be found effectively. As a corollary we solve an open problem by Gurari and Ibarra: The equivalence problem for finite valued finite transducers is decidable. This is the first time the equivalence problem is shown to be decidable for a larger class of multivalued transducers.

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