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<Paper uid="E93-1045">
  <Title>The Use of Shared Forests in Tree Adjoining Grammar Parsing*</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> We study parsing of tree adjoining grammars (tag) with particular emphasis on the use of shared forests to represent all the parse trees deriving a well-formed string. Following Billot and Lang \[1989\] and Lang \[1992\] we use grammars as a means of recording all parses. Billot and Lang used context-free grammars (cfg) for representing all parses in a cfg parser demonstrating that a shared forest grammar can be viewed as a specialization of the grammar for the given input string. Lang \[1992\] extended this approach considering both the recognition problem as well as the representation of all parses and suggests how this can be applied to tag.</Paragraph>
    <Paragraph position="1"> This paper examines this approach to tag parsing in greater detail. In particular, we show that *We are very grateful to Bernard Lang for helpful discussions.</Paragraph>
    <Paragraph position="2"> there are two distinct ways of representing the parse forest. One possibility is to use linear indexed grammars (lig), a formalism that is e~uivalent to tag \[Vijay-Shanker and Weir, in pressa\]. The use of lig is not surprising in that we would expect to be able to represent parses of a formalism in an equivalent formalism. However, we also show that there is a second way of representing parses that makes use ofa cfg.</Paragraph>
    <Paragraph position="3"> The work presented in this paper is intended to give a general framework for studying tag parsing.</Paragraph>
    <Paragraph position="4"> The schemes using lig and cfg to represent parses can be seen to underly most of the existing tag parsing algorithms.</Paragraph>
    <Paragraph position="5"> We begin with brief definitions of the tag and lig formalisms. This is followed by a discussion of the methods for cfg recognition and the representation of parses trees that were described in \[Billot and Lang, 1989; Lang, 1992\]. In the remainder of the paper we examine how this approach can be applied to tag. We first consider the representation of parses using a cfg and give the space and time complexity of recognition and extraction of parses using this representation. We then consider the same issues where lig is used as the formalism for representing parses. We conclude by comparing these results with those for existing tag parsing algorithms.</Paragraph>
  </Section>
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