Semi-synchronously rational relations generalise synchronised rational relations in a natural way. We discuss here some of
their basic properties, among them a “Cobham–Semenov-like” dichotomy theorem. Our main result is a characterisation of bijective
semi-synchronously rational transductions as those bijections mapping regular relations to regular ones and non-regular relations
to non-regular ones.
Work done while affiliated with RWTH Aachen and partially supported by the project ANR-06-MDCA DocFlow.