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<Paper uid="P99-1059">
  <Title>Efficient Parsing for Bilexical Context-Free Grammars and Head Automaton Grammars*</Title>
  <Section position="9" start_page="462" end_page="462" type="concl">
    <SectionTitle>
9 Final remarks
</SectionTitle>
    <Paragraph position="0"> We have formally described, and given faster parsing algorithms for, three practical grammatical rewriting systems that capture dependencies between pairs of words. All three systems admit naive O(n 5) algorithms. We give the first O(n 4) results for the natural formalism of bilexical context-free grammar, and for AIshawi's (1996) head automaton grammars. For the usual case, split head automaton grammars or equivalent bilexical CFGs, we replace the O(n 3) algorithm of (Eisner, 1997) by one with a smaller grammar constant. Note that, e.g., all senses would restore the g2 factor. Indeed, this approach gives added flexibility: a word's sense, unlike its choice of flip state, is visible to the HA that reads it.</Paragraph>
    <Paragraph position="1"> three models in (Collins, 1997) are susceptible to the O(n 3) method (cf. Collins's O(nh)).</Paragraph>
    <Paragraph position="2"> Our dynamic programming techniques for cheaply attaching head information to derivations can also be exploited in parsing formalisms other than rewriting systems. The authors have developed an O(nT)-time parsing algorithm for bilexicalized tree adjoining grammars (Schabes, 1992), improving the naive O(n s) method.</Paragraph>
    <Paragraph position="3"> The results mentioned in SS6 are related to the closure property of CFGs under generalized sequential machine mapping (Hopcroft and Ullman, 1979). This property also holds for our class of bilexical CFGs.</Paragraph>
  </Section>
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