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<Paper uid="P06-1052">
  <Title>Sydney, July 2006. c(c)2006 Association for Computational Linguistics An Improved Redundancy Elimination Algorithm for Underspecified Representations</Title>
  <Section position="8" start_page="415" end_page="415" type="concl">
    <SectionTitle>
6 Conclusion
</SectionTitle>
    <Paragraph position="0">  Wepresentedanalgorithmforredundancyelimination on underspecified chart representations. This algorithm successively deletes eliminable splits from the chart, which reduces the set of described readings while making sure that at least one representative of each original equivalence class remains. Equivalence is defined with respect to a certain class of rewriting systems; this definition approximates semantic equivalence of the described formulas and fits well with the underspecification setting. The algorithm runs in polynomial time in the size of the chart.</Paragraph>
    <Paragraph position="1"> We then evaluated the algorithm on the Rondanecorpusandshowedthatitisusefulinpractice: null the median number of readings drops from 56 to 4, and the maximum individual reduction factor is 666.240. The algorithm achieves complete reduction for 56% of all sentences. It does this in negligible runtime; even the most difficult sentences in the corpus are reduced in a matter of seconds, whereas the enumeration of all readings would take about a year. This is the first corpus evaluation of a redundancy elimination in the literature. The algorithm improves upon previous work (KollerandThater,2006)inthatiteliminatesmore splits from the chart. It is an improvement over earlier algorithms for enumerating irredundant readings (Vestre, 1991; Chaves, 2003) in that it maintains underspecifiedness; note that these earlier papersnevermadeanyclaimswithrespectto,oreval- null uated, completeness.</Paragraph>
    <Paragraph position="2"> There are a number of directions in which the present algorithm could be improved. We are currently pursuing some ideas on how to improve the completeness of the algorithm further. It would also be worthwhile to explore heuristics for the order in which splits of the same subgraph are eliminated. The present work could be extended to allow equivalence with respect to arbitrary rewrite systems.Mostgenerally,wehopethatthemethods developed here will be useful for defining other elimination algorithms, which take e.g. full world knowledge into account.</Paragraph>
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