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A uniformization of a binary relation is a function that is contained in therelation and has the same domain as the relation. The synthesis problem asksfor effective uniformization for classes of relations and functions that can beimplemented in a specific way.  We consider the synthesis problem for automatic relations over finite words(also called regular or synchronized rational relations) by functionsimplemented by specific classes of sequential transducers.  It is known that the problem "Given an automatic relation, does it have auniformization by a subsequential transducer?" is decidable in the two variantswhere the uniformization can either be implemented by an arbitrarysubsequential transducer or it has to be implemented by a synchronoustransducer. We introduce a new variant of this problem in which the allowedinput/output behavior of the subsequential transducer is specified by a set ofsynchronizations and prove decidability for a specific class ofsynchronizations.

Uniformization Problems for Synchronizations of Automatic Relations on Words