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Alexander Koller and Marco Kuhlmann. Decomposing TAG Parsing Algorithms Using Simple Algebraizations. In Proceedings of the 11th International Workshop on Tree Adjoining Grammars and Related Formalisms (TAG+), pages 135–143, Paris, France, 2012.
We review a number of different `algebraic' perspectives on TAG and STAG in the framework of interpreted regular tree grammars (IRTGs). We then use this framework to derive a new parsing algorithm for TAGs, based on two algebras that describe strings and derived trees. Our algorithm is extremely modular, and can easily be adapted to the synchronous case.