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

Abstract

An NP-hardness proof for nonlocal MCTAG by Rambow and Satta (1992), based on Dahlhaus and Warmuth (1986), is extended to some restrictions of that formalism. It is found that there are NP-hard grammars among nonlocal MCTAGs even if the following restrictions are imposed: every tree in every tree set has a lexical anchor; every tree set may contain at most two trees; in every such tree set, there is a dominance link between the foot node of one tree and the root node of the other tree and this dominance link must be obeyed in the derived tree. This is the version of MCTAG used in Becker, Joshi, and Rambow (1991). The lexicalization restriction makes the grammar class NPcomplete.

A polynomial-time parsing algorithm for TT-MCTAG

“…For some of the above formalisms the word recognition problem is NP-hard. This has been shown for non-local MCTAG (Rambow and Satta, 1992), even in the lexicalized case (Champollion, 2007). Some others generate only polynomial languages but their generative capacity is too limited to deal with all natural language phenomena.…”