A note on finite-valued and finitely ambiguous transducers

We look at some decision problems concerning nondeterministic finite transducers. The problems concern finite-valuedness, finite ambiguity, equivalence, etc. For a fixedk, we give a polynomial time algorithm for deciding whether or not a transducer isk-valued. The result holds when “valued” is replaced by “ambiguous”. In fact, the following problems are decidable: 1) Given a transducer, is itk-ambiguous for somek? 2) Given two finitely ambiguous transducers, are they equivalent? For unambiguous transducers, equivalence is decidable in polynomial time.

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