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We place synchronous tree-adjoining grammars and tree transducers in the single overarching framework of bimorphisms, continuing the unification of synchronous grammars and tree transducers initiated by Shieber (2004). Along the way, we present a new definition of the tree-adjoining grammar derivation relation based on a novel direct inter-reduction of TAG and monadic macro tree transducers. Tree transformation systems such as tree transducers and synchronous grammars have seen renewed interest, based on a perceived relevance to new applications, such as importing syntactic structure into statistical machine translation models or founding a formalism for speech command and control. . | Unifying Synchronous Tree-Adjoining Grammars and Tree Transducers via Bimorphisms Stuart M. Shieber Division of Engineering and Applied Sciences Harvard University Cambridge MA USA shieber@deas.harvard.edu Abstract We place synchronous tree-adjoining grammars and tree transducers in the single overarching framework of bimorphisms continuing the unification of synchronous grammars and tree transducers initiated by Shieber 2004 . Along the way we present a new definition of the tree-adjoining grammar derivation relation based on a novel direct inter-reduction of TAG and monadic macro tree transducers. Tree transformation systems such as tree transducers and synchronous grammars have seen renewed interest based on a perceived relevance to new applications such as importing syntactic structure into statistical machine translation models or founding a formalism for speech command and control. The exact relationship among a variety of formalisms has been unclear with a large number of seemingly unrelated formalisms being independently proposed or characterized. An initial step toward unifying the formalisms was taken Shieber 2004 in making use of the formal-language-theoretic device of bimorphisms previously used to characterize the tree relations definable by tree transducers. In particular 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. In this work we show how the bimorphism framework can be used to capture a more powerful formalism synchronous tree-adjoining grammars providing a further uniting of the various and disparate formalisms. After some preliminaries Section 1 we begin by recalling the definition of tree-adjoining grammars and synchronous tree-adjoining grammars Section 2 . We turn then to a set of known results relating context-free languages tree .
