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<Paper uid="P97-1042">
  <Title>Compiling Regular Formalisms with Rule Features into Finite-State Automata</Title>
  <Section position="7" start_page="334" end_page="334" type="ackno">
    <SectionTitle>
Acknowledgments
</SectionTitle>
    <Paragraph position="0"> I would like to thank Richard Sproat for commenting on an earlier draft. Many of the anonymous reviewers' comments proofed very useful. Mistakes, as always, remain mine.</Paragraph>
    <Paragraph position="1"> the subtractive approach of (Grimley-Evans, Kiraz, and Pulman, 1996).</Paragraph>
    <Paragraph position="2"> The statistics of the usage of computationally expensive operations - viz., intersection (quadratic complexity) and determinization (exponential complexity) - in both algorithms are summarized in Figure 4 (KK = Kaplan and Kay, EKP = Grimley-Evans, Kiraz and Pulman). Note that complementation requires determinization, and subtraction requires one intersection and one complementation since A- B = An B (27) Although statistically speaking the number of operations used in (Grimley-Evans, Kiraz, and Pulman, 1996) is less than the ones used in (Kaplan and Kay, 1994), only an empirical study can resolve the issue as the following example illustrates. Consider the expression A =al Ua2U...Uan and the De Morgan's law equivalent</Paragraph>
    <Paragraph position="4"> The former requires only one complement which results in one determinization (since the automata must be determinized before a complement is computed). The latter not only requires n complements, but also n - 1 intersections. The worst-case analysis clearly indicates that computing A is much less expensive than computing B. Empirically, however, this is not the case when n is large and ai is small, which is usually the case in rewrite rules. The reason lies in the fact that the determinization algorithm in the former expression applies on a machine which is by far larger than the small individual machines present in the latter expression, is Another aspect of rule features concerns the morphotactic unification of lexical entries. This is best aSThis important difference was pointed out by one of the anonymous reviewers whom I thank.</Paragraph>
  </Section>
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