In this paper we present a polynomial time parsing algorithm for Combinatory Categorial Grammar. The recognition phase extends the CKY algorithm for CFG. The process of generating a representation of the parse trees has two phases. Initially, a shared forest is build that encodes the set of all derivation trees for the input string. This shared forest is then pruned to remove all spurious ambiguity.
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Vijay‐Shanker et al. (1990) studied this question.