Long-distance scrambling and tree adjoining grammars

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

“…In contrast, Becker, Joshi, and Rambow (1991) argue that longdistance scrambling in German is even beyond the power of LCFRS, a formalism which was introduced in Weir (1988) and which remains the best known formal characterization of the only roughly defined MCSG class. LCFRS are equally powerful to set-local MCTAG, in the sense that for each set-local MCTAG, there is a strongly equivalent LCFRS.…”

“…2 However, there is some reason to believe that German scrambling is in fact more restricted than described in Becker, Joshi, and Rambow (1991) and that scrambling might not be beyond LCFRS after all (see section 6). For a polynomially parsable TAG variant claimed to assign the right structural descriptions to German scrambling, see Kallmeyer (2005b); cf.…”

“…4 MCTAG-DL have already been used by Kroch and Joshi (1987) for the analysis of extraposition in English. But unlike Becker, Joshi, and Rambow (1991), they impose the additional constraint of tree-locality. Dominance links in connection with tree-locality or set-locality can be simulated by choosing appropriate node labels (Kallmeyer, 2005a).…”

“…One of the first proposals to deal with the German scrambling data used nonlocal MCTAG with dominance links (MCTAG-DL) (Becker, Joshi, and Rambow, 1991). In this modification of nonlocal MCTAG, an additional requirement is added: in the final derived tree, the foot node of one of the components of an auxiliary set has to dominate the root node of the other component in the same auxiliary set.…”

“…LCFRS are equally powerful to set-local MCTAG, in the sense that for each set-local MCTAG, there is a strongly equivalent LCFRS. This means that if one accepts Becker, Joshi, and Rambow (1991)'s argument, then set-local MCTAG, as well as a number of equivalent or less powerful formalisms such as head grammars (Pollard, 1984) and combinatory categorial grammars (Steedman, 1988) that can be classified as LCFRS (Joshi, Vijay-Shanker, and Weir, 1991), are no longer in the game. 2 Despite these results, one can still hope to find a language class that is adequate for natural language and has the property of being parsable in polynomial time.…”