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<Paper uid="P97-1057">
  <Title>String Transformation Learning</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Ordered sequences of rewriting rules are used in several applications in natural language processing, including phonological and morphological systems (Kaplan and Kay, 1994), morphological disambiguation, part-of-speech tagging and shallow syntactic parsing (Brill, 1995), (Karlsson et ah, 1995).</Paragraph>
    <Paragraph position="1"> In (Brill, 1995) a learning paradigm, called error-driven learning, has been introduced for automatic induction of a specific kind of rewriting rules called transformations, and it has been shown that the achieved accuracy of the resulting transformation systems is competitive with that of existing systems.</Paragraph>
    <Paragraph position="2"> In this work we further elaborate on the error-driven learning paradigm. Our main contribution is summarized in what follows. We consider some families of transformations and design efficient algorithms for the associated learning problem that improve existing methods. Our results are achieved by exploiting a data structure originally introduced in this work. This allows us to simultaneously represent and test the search space of all possible transformations. The transformations we investigate make use of classes of symbols, in order to generalize regularities in rule applications. We also show that when an unbounded number of these symbol classes are allowed within a transformation, then the associated learning problem becomes NP-hard.</Paragraph>
    <Paragraph position="3"> The notation we use in the remainder of the paper is briefly introduced here. ~3 denotes a fixed, finite alphabet and e the null string. E* and E+ are the set of all strings and all non-null strings over E, respectively. Let w 6 E*. We denote by Iwl the length ofw. Let w = uxv; uis aprefix and v is a suffix of w; when x is non-null, it is called a factor of w. The suffix of w of length i is denoted suffi(w), for O &lt; i _&lt; Iwl. Assume that x is non-null, and w = uixsuffi(w ) for ~ &gt; 0 different values of i but not for ~ + 1, or x is not a factor of w and ~ = 0.</Paragraph>
    <Paragraph position="4"> Then we say that ~ is the statistic of factor z in w.</Paragraph>
  </Section>
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