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<Paper uid="P90-1036">
  <Title>AN EFFICIENT PARSING ALGORITHM FOR TREE ADJOINING GRAMMARS</Title>
  <Section position="11" start_page="290" end_page="291" type="concl">
    <SectionTitle>
5 SUMMARY
</SectionTitle>
    <Paragraph position="0"> In the application domain of natural language processing, the execution time in an average case is of great interest as well. For the new parsing algorithm, a result is not yet known, but in basic considerations the main idea is to take the depth of analyzed parts of derivation trees as a constant term to come up with a result of O(n3).</Paragraph>
    <Paragraph position="1"> Actually, an implementation of the presented formalism exists written in Common LISP on a Hewlett Packard machine of the 9000 series (for more details about the implementation see \[Buschauer et al. 89\]). To give an idea of the response time, the analysis of a sentence of about 10 to 15 words and a grammar of about 20 to 30 elementary trees takes at most 6 milliseconds. Currently, this implementation is extended to build a workbench supporting a linguist in writing and testing large TAG grammars (respectively TAGs with Unification).</Paragraph>
    <Paragraph position="2"> Finally, other approaches for TAG parsing should be mentioned and compared with the presented result. In the literature, the two Earleybased approaches of Schabes and Joshi (see \[Schabes, Joshi 89\]) and of Lang (\[Lang 86\]) are proposed. The lowest upper time bound for the Schabes.Joshi approach is O(n 9) and for the approach of Lang O(n6). But both algorithms come up with better results in the best and in the average case. In the framework of parallel parsing, results for TAGs are also proposed. In \[Palis et al. 87\] a linear time approach on O(n 5) processors and in \[Palis, Shende 88\] a sublinear (O(log 2 n)) algorithm is described.</Paragraph>
    <Paragraph position="3"> One future perspective is to parallelize the new approach by the same method so that the expected result should be a linear time bound on O(n 2) processors. More concretely, an optimal layout for two processors is looked for, where independent subtrees have to be specified (candidates are not always total innermost trees, e.g., if only one TAG derivation exists where all innermost trees are nested).</Paragraph>
    <Paragraph position="4"> Further on, we concentrate on appropriate extensions of the TAG formalism for analysis as well as generation of natural language with the ambitious aim to verify that TAGs (in some extension) are appropriate for a bidirectional and integrated description of syntax, semantics and pragmatics.</Paragraph>
  </Section>
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