On the Complexity of CCG Parsing

TL;DR

This paper proves that parsing in the Vijay-Shanker and Weir (1994) formalism of CCG is inherently exponential in the worst case when considering grammar size, unlike some related formalisms like TAG.

Contribution

It establishes the worst-case exponential parsing complexity for this CCG formalism, highlighting a key difference from similar mildly context-sensitive grammars.

Findings

Parsing complexity is exponential in grammar size.

Contrasts with polynomial parsing in TAG.

Provides insights into the computational limits of CCG.

Abstract

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 take in the worst case exponential time when the size of the grammar, and not only the length of the input sentence, is included in the analysis. This 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 results contribute to a refined understanding of the class of mildly context-sensitive grammars, and inform the search for new, mildly context-sensitive versions of CCG.