Polynomial Parsing of Extensions of Context-Free Grammars

Abstract

In (Joshi, Vijay-Shanker, & Weir, 1989; Vijay-Shanker, Weir, & Joshi, 1986; Weir & Joshi, 1988) we have shown that Combinatory Categorial Grammars (CCG), Head Grammars (HG), Linear Indexed Grammars (LIG), and Tree Adjoining Grammars (TAG) are weakly equivalent, i.e., they generate the same class of string languages. Although it is known that there are polynomial-time recognition algorithms for HG and TAG (Pollard, 1984; Vijay-Shanker & Joshi, 1985), there are no known polynomial-time recognition algorithms that work directly with CCG or LIG. In this chapter we present polynomial-time recognition algorithms for LIG and CCG that resemble the CKY algorithm for Context-Free Grammars (CFG) (Kasami, 1965; Younger, 1967). We also show how this approach can be adapted for TAG.