An NP-hardness proof for non-local Multicomponent Tree Adjoining Grammar
(MCTAG) by Rambow and Satta (1st International Workshop on Tree
Adjoining Grammers 1992), based on Dahlhaus and Warmuth (in J Comput
Syst Sci 33:456–472, 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.
(Proceedings of the 5th conference of the European chapter of the
Association for Computational Linguistics 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
