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<Paper uid="E95-1011">
  <Title>A Tractable Extension of Linear Indexed Grammars</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Unification-based grammar formalisms can be viewed as generalizations of Context-Free Grammars (CFG) where the nonterminal symbols are replaced by an infinite domain of feature structures. Much of their popularity stems from the way in which syntactic generalization may be elegantly stated by means of constraints amongst features and their values. Unfortunately, the expressivity of these formalisms can have undesirable consequences for their processing. In naive implementations of unification grammar parsers, feature structures play the same role as nonterminals in standard context-free grammar parsers. Potentially large feature structures are stored at intermediate steps in the computation, so that the space requirements of the algorithm are expensive. Furthermore, the need to perform non-destructive unification means that a large proportion of the processing time is spent copying feature structures.</Paragraph>
    <Paragraph position="1"> One approach to this problem is to refine parsing algorithms by developing techniques such as restrictions, structure-sharing, and lazy unification that reduce the amount of structure that is stored and hence the need for copying of features structures (Shieber, 1985; Pereira, 1985; Karttunen and Kay, 1985; Wroblewski, 1987; Gerdemann, 1989; Godden, 1990; Kogure, 1990; Emele, 1991; Tomabechi, 1991; Harrison and Ellison, 1992)). While these techniques can yield significant improvements in performance, the generality of unification-based grammar formalisms means that there are still cases where expensive processing is unavoidable. This approach does not address the fundamental issue of the tradeoff between the descriptive capacity of a formalism and its computational power.</Paragraph>
    <Paragraph position="2"> In this paper we identify a set of constraints that can be placed on unification-based grammar formalisms in order to guarantee the existence of polynomial time parsing algorithms. Our choice of constraints is motivated by showing how they generalize constraints inherent in Linear Indexed Grammar (l_lG). We begin by describing how constraints inherent in I.IG admit tractable processing algorithms and then consider how these constraints can be generalized to a formalism that manipulates trees rather than stacks. The constraints that we identify for the tree-based system can be regarded equally well as constraints on unification-based grammar formalisms such as PArR (Shieber, 1984).</Paragraph>
  </Section>
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