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<Paper uid="W06-2929">
  <Title>Vine Parsing and Minimum Risk Reranking for Speed and Precision[?]</Title>
  <Section position="4" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 Notation
</SectionTitle>
    <Paragraph position="0"> Let a sentence x = &lt;x1,x2,...,xn&gt; , where each xi is a tuple containing a part-of-speech tag ti and a word wi, and possibly more information.1 x0 is a special wall symbol, $, on the left. A dependency tree y is defined by three functions: yleft and yright (both {0,1,2,...,n} - 2{1,2,...,n}) that map each word to its sets of left and right dependents, respectively, and ylabel : {1,2,...,n} -D, which labels the relationship between word i and its parent from label set D. In this work, the graph is constrained to be a projective tree rooted at $: each word except $ has a single parent, and there are no cycles or crossing dependencies. Using a simple dynamic program to find the minimum-error projective parse, we find that assuming projectivity need not harm accuracy very much (Tab. 1, col. 3).</Paragraph>
  </Section>
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