Efficiently Parsing with the Product-Free Lambek Calculus

This paper provides a parsing algorithm for the Lambek calculus which is polynomial time for a more general fragment of the Lambek calculus than any previously known algorithm. The algorithm runs in worst-case time O(n5) when restricted to a certain fragment of the Lambek calculus which is motivated by empirical analysis. In addition, a set of parameterized inputs are given, showing why the algorithm has exponential worst-case running time for the Lambek calculus in general.

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