On Equivalence and Uniformisation Problems for Finite Transducers

TL;DR

This paper explores decidability of stronger variants of equivalence, inclusion, and uniformisation problems for finite transducers using transducer resynchronisation, and extends results to finite-valued and deterministic transductions.

Contribution

It introduces decidability results for stronger variants of classical problems and extends decidability of sequential uniformisation to finite-valued and deterministic transductions.

Findings

Decidability of stronger inclusion, equivalence, and uniformisation variants.

Decidability of sequential uniformisation for finite-valued transductions.

Decidability of sequential uniformisation for deterministic transductions.

Abstract

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper, we investigate stronger variants of inclusion, equivalence and sequential uniformisation, based on a general notion of transducer resynchronisation, and show their decidability. We also investigate the classes of finite-valued rational transductions and deterministic rational transductions, which are known to have a decidable equivalence problem. We show that sequential uniformisation is also decidable for them.