Decidability results for synthesizing rational resynchronizers from functional one-way transducers and regular resynchronizers from unambiguous two-way transducers, with undecidability for relational one-way transducers.
Origin-equivalence of two-way word transducers is in PSPACE
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On Synthesis of Resynchronizers for Transducers
Decidability results for synthesizing rational resynchronizers from functional one-way transducers and regular resynchronizers from unambiguous two-way transducers, with undecidability for relational one-way transducers.