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<Paper uid="E91-1006">
  <Title>BIDIRECTIONAL PARSING OF LEXICALIZED TREE ADJOINING GRAMMARS*</Title>
  <Section position="7" start_page="0" end_page="0" type="concl">
    <SectionTitle>
6, Discussion
</SectionTitle>
    <Paragraph position="0"> Within the perspective of Lexicalized TAGs, known methods for TAGs recognition/parsing present some limitations: these methods behave in a left-to-right fashion (Schabes and Joshi, 1988) or they are purely bottom-up (Vijay-Shanker and Joshi, 1985, Harbusch, 1990), hence they cannot take advantage of anchor information in a direct way. The presented algorithm directly exploits both the advantages of lexicalization mentioned in the paper by Schabes and Joshi (1989), i.e. grammar filtering and bottom-up information. In fact, such an algorithm starts partial analyses from the anchor elements, directly selecting the relevant trees in the grammar, and then it proceeds in both directions, climbing to the roots of these trees and predicting the rest of the structures in a top-down fashion. These capabilities make the algorithm attractive from the perspective of linguistic information processing, even if it does not improve the worst-case time bounds of already known TAGs parsers.</Paragraph>
    <Paragraph position="1"> The studied algorithm recognizes auxiliary trees without considering the substring dominated by the foot node, as is the case of the CYK-like algorithm in Vijay-Shanker and Joshi (1985). More precisely, Case 3 in the procedure Left-expander nondeterministically jumps over such a substring. Note that the alternative solution, which consists in waiting for possible analyses subsumed by the foot node, would prevent the algorithm from recognizing particular configurations, due to the bidirectional behaviour of the method (examples are left to the reader). On the contrary, Earley-like parsers for TAGs (Lang, 1990, Schabes, 1990) do care about substrings dominated by the foot node. However, these algorithms are forced to start at each foot node the recognition of all possible subtrees of the elementary trees whose roots can be the locus of an adjunction.</Paragraph>
    <Paragraph position="2"> In this work, we have discussed a theoretical schema for the parser, in order to study its formal properties. In practical cases, such an algorithm could be considerably improved. For example, the above mentioned guess in Case 3 of the procedure Left-expander could take advantage of look-ahead techniques. So far, we have not addressed topics such as substitution or on-line recognition. Our algorithm can be easily modified in these directions, adopting the same proposals advanced in (Schabes and Joshi, 1988).</Paragraph>
    <Paragraph position="3"> Finally, a parser for Lexicalized TAGs can be obtained from Algorithm 1. To this purpose, it suffices to store elements in IS into the recognition matrix T along with a list of pointers to those entries that caused such elements to be placed in the matrix. Using this additional information, it is not difficult to exhibit an algorithm for the construction of the desired parser(s).</Paragraph>
  </Section>
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