An initial step toward unifying the formalisms was taken (Shieber, 2004) in making use of the formallanguage-theoretic device of bimorphisms, previously used to characterize the tree relations definable by tree transducers.
the tree relations definable by synchronous tree-substitution grammars (STSG) were shown to be just those definable by linear complete bimorphisms, thereby providing for the first time a clear relationship between synchronous grammars and tree transducers.