Lexicalized Non-Local MCTAG with Dominance Links is NP-Complete

Abstract An NP-hardness proof for non-local Multicomponent Tree Adjoining Grammar (MCTAG) by Rambow and Satta (1992), based on Dahlhaus and Warmuth (1986), is extended to some linguistically relevant restrictions of that formalism. It is found that there are NP-hard grammars among non-local MCTAGs even if any or all of the following restrictions are imposed: (i) lexicalization: every tree in the grammar contains a terminal; (ii) dominance links: every tree set contains at most two trees, and in every such tree set, there is a link between the foot node of one tree and the root node of the other tree, indicating that the former node must dominate the latter in the derived tree. This is the version of MCTAG proposed in Becker et al (1991) to account for German long-distance scrambling. This result restricts the field of possible candidates for an extension of Tree Adjoining Grammar that would be both mildly context-sensitive and linguistically adequate.