The ability to represent cross-serial dependencies is one of the central features of Tree Adjoining Grammar (TAG). The class of dependency structures representable by lexicalized TAG derivations can be captured by two graph-theoretic properties: a bound on the gap degree of the structures, and a constraint called well-nestedness. In this paper, we compare formalisms from two strands of extensions to TAG in the context of the question, how they behave with respect to these constraints. In particular, we show that multi-component TAG does not necessarily retain the well-nestedness constraint, while this constraint is inherent to Coupled Context-Free Grammar (Hotz and Pitsch, 1996).
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