Parsing for Semidirectional Lambek Grammar is NP-Complete
<|reference_start|>Parsing for Semidirectional Lambek Grammar is NP-Complete: 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.<|reference_end|>
@article{doerre1996parsing,
    title={Parsing for Semidirectional Lambek Grammar is NP-Complete},
    author={Jochen Doerre (Univ. Stuttgart)},
    journal={Proceedings ACL '96 (Santa Cruz)},
    year={1996},
    archivePrefix={arXiv},
    eprint={cmp-lg/9605016},
    primaryClass={cmp-lg cs.CL}
}