  Regular synchronization languages can be used to define rational relations of
finite words, and to characterize subclasses of rational relations, like
automatic or recognizable relations. We provide a systematic study of the
decidability of uniformization and definability problems for subclasses of
rational relations defined in terms of such synchronization languages. We
rephrase known results in this setting and complete the picture by adding
several new decidability and undecidability results.
