One-way resynchronizability of word transducers

TL;DR

This paper establishes the decidability of whether a non-deterministic two-way word transducer can be resynchronized into an equivalent one-way transducer under origin semantics, contrasting with classical undecidability results.

Contribution

It introduces a decidability result for resynchronizing two-way transducers to one-way transducers in origin semantics, expanding understanding of transducer equivalence.

Findings

Decidable resynchronization of two-way to one-way transducers

Contrast with classical semantics where equivalence is undecidable

Characterization of bounded, regular resynchronizers

Abstract

The origin semantics for transducers was proposed in 2014, and 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.