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<Paper uid="P96-1013">
  <Title>Parsing for Semidirectional Lambek Grammar is NP-Complete</Title>
  <Section position="1" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
Abstract
</SectionTitle>
    <Paragraph position="0"> We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call semidirectional. In semidirectional Lambek calculus SD\[ 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. SD\[ grammars are able to generate each context-free language and more than that. We show that the parsing problem for semidireetional Lambek Grammar is NP-complete by a reduction of the 3-Partition problem.</Paragraph>
    <Paragraph position="1"> Key words: computational complexity, Lambek Categorial Grammar</Paragraph>
  </Section>
class="xml-element"></Paper>