A Left Corner Parser for Tree Adjoining Grammars

Tabular parsers can be de£ned as deduction systems where formulas, called items, are sets of complete or incomplete constituents (Sikkel, 1997; Shieber, Schabes and Pereira, 1995). Formally, given an input string w = a1 . . . an with n ≥ 0 and a grammar G, a parser IP is a tuple (I,H,D) where I is a set of items, H is a set of hypothesis ([ai, i − 1, i] with 1 ≤ i ≤ n) that encodes the input string, and D is a set of deduction steps that determines how items are combined in order to deduce new items. The deductive approach allows us to establish relations between two parsers in a formal way. One of the most interesting relations between parsers are £lters because they can be used to improve the performance of tabular parsers in practical cases. The application of a £lter to a parser yields a new parser which performs less deductions or contracts sequences of deductions to single deduction steps. One well-known example of a £lter is the relation between Earley and Left Corner (LC) parsers for ContextFree Grammars (CFGs). A LC parser reduces the number of items deduced by Earley’s parser using the left corner relation. Given a CFG, the left corner of a non-terminal symbol A is the terminal or non-terminal symbol X if and only if there exists a production A → Xν in the grammar, where ν is a sequence of symbols. In the case of A → e, we consider e as the left corner of A. The notion of the left corner relation allow us to rule out the prediction performed on X by an Earley’s parser. Most tabular parsers for Tree Adjoining Grammars (TAGs) are extensions of well-known tabular parser for CFGs. For example, we can cite a number of tabular parsers for TAGs de£ned on the basis of the Earley’s algorithm (Alonso Pardo et al., 1999; Lang, 1990; Joshi and Schabes, 1997; Nederhof, 1999). Although several approaches have been described to improve the performance of TAGs parsers, most of them based on restrictions in the formalism (Schabes and Waters, 1995) or compilation into £nite-state automata (Evans and Weir, 1998), to the best of our knowledge, no attempt has been made to improve the practical performance of Earley-based parsers for TAGs by introducing the left-corner relation.