One-way Resynchronizability of Word Transducers

Abstract

The origin semantics for transducers was proposed in 2014, and it led to various characterizations and decidability results that are in contrast with the classical semantics. In this paper we add a further decidability result for characterizing transducers that are close to one-way transducers in the origin semantics. We show that it is decidable whether a non-deterministic two-way word transducer can be resynchronized by a bounded, regular resynchronizer into an origin-equivalent one-way transducer. The result is in contrast with the usual semantics, where it is undecidable to know if a non-deterministic two-way transducer is equivalent to some one-way transducer.

Resynchronized Uniformization and Definability Problems for Rational Relations

“…For rational relations, the problem becomes undecidable, see (Carayol and Löding, 2014, Theorem 17) (however, each rational relation has a uniformization by a rational function, see Sakarovitch (2009), which needs not be subsequential). (i) The introduction of this measure has triggered similar work on two-way transducers, see Bose et al (2018Bose et al ( , 2019.…”