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<Paper uid="P97-1002">
  <Title>Fast Context-Free Parsing Requires Fast Boolean Matrix Multiplication</Title>
  <Section position="1" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
Abstract
</SectionTitle>
    <Paragraph position="0"> Valiant showed that Boolean matrix multiplication (BMM) can be used for CFG parsing. We prove a dual result: CFG parsers running in time O(\[Gl\[w\[ 3-e) on a grammar G and a string w can be used to multiply m x m Boolean matrices in time O(m3-e/3).</Paragraph>
    <Paragraph position="1"> In the process we also provide a formal definition of parsing motivated by an informal notion due to Lang. Our result establishes one of the first limitations on general CFG parsing: a fast, practical CFG parser would yield a fast, practical BMM algorithm, which is not believed to exist.</Paragraph>
  </Section>
class="xml-element"></Paper>