On the Complexity of CCG Parsing

We study the parsing complexity of Combinatory Categorial Grammar (CCG) in the formalism of Vijay-Shanker and Weir (1994). As our main result, we prove that any parsing algorithm for this formalism will necessarily take exponential time when the size of the grammar, and not only the length of the input sentence, is included in the analysis. This result sets the formalism of Vijay-Shanker and Weir (1994) apart from weakly equivalent formalisms such as Tree-Adjoining Grammar (TAG), for which parsing can be performed in time polynomial in the combined size of grammar and input sentence. Our proof highlights important differences between the formalism of Vijay-Shanker and Weir (1994) and contemporary incarnations of CCG.