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Parsing for Semidirectional Lambek Grammar is NP-Complete

Jochen Doerre
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Abstract

We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call {\em semidirectional}. In semidirectional Lambek calculus $\SDL$ there is an additional non-directional abstraction rule allowing the formula abstracted over to appear anywhere in the premise sequent's left-hand side, thus permitting non-peripheral extraction. $\SDL$ grammars are able to generate each context-free language and more than that. We show that the parsing problem for semidirectional Lambek Grammar is NP-complete by a reduction of the 3-Partition problem.

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Jochen Doerre. 1996-05-10. Parsing for Semidirectional Lambek Grammar is NP-Complete. https://arxiv.org/abs/cmp-lg/9605016

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