On the Complexity of CCG Parsing
This work provides a refined understanding of mildly context-sensitive grammars, informing the search for new CCG variants, but it is incremental as it focuses on complexity analysis rather than practical improvements.
The paper proves that parsing Combinatory Categorial Grammar (CCG) in the Vijay-Shanker and Weir formalism requires exponential time in the worst case when considering grammar size, unlike weakly equivalent formalisms like Tree-Adjoining Grammar which allow polynomial-time 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 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.