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<Paper uid="E95-1015">
  <Title>VP VB NP NP PP PP IN NP VP VBG NN</Title>
  <Section position="1" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
Abstract
</SectionTitle>
    <Paragraph position="0"> We deal with the question as to whether there exists a polynomial time algorithm for computing the most probable parse tree of a sentence generated by a data-oriented parsing (DOP) model. (Scha, 1990; Bod, 1992, 1993a). Therefore we describe DOP as a stochastic tree-substitution grammar (STSG). In STSG, a tree can be generated by exponentially many derivations involving different elementary trees. The probability of a tree is equal to the sum of the probabilities of all its derivations.</Paragraph>
    <Paragraph position="1"> We show that in STSG, in contrast with stochastic context-free grammar, the Viterbi algorithm cannot be used for computing a most probable tree of a string. We propose a simple modification of Viterbi which allows by means of a &amp;quot;select-random&amp;quot; search to estimate the most probable tree of a string in polynomial time.</Paragraph>
    <Paragraph position="2"> Experiments with DOP on ATIS show that only in 68% of the cases, the most probable derivation of a string generates the most probable tree of that string. Therefore, the parse accuracy obtained by the most probable trees (96%) is dramatically higher than the parse accuracy obtained by the most probable derivations (65%).</Paragraph>
    <Paragraph position="3"> It is still an open question whether the most probable tree of a string can be deterministically computed in polynomial time.</Paragraph>
  </Section>
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