  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.
