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<Paper uid="P95-1002">
  <Title>Automatic Induction of Finite State Transducers for Simple Phonological Rules</Title>
  <Section position="7" start_page="12" end_page="13" type="evalu">
    <SectionTitle>
6 Results and Discussion
</SectionTitle>
    <Paragraph position="0"> We tested our induction algorithm using a synthetic corpus of 99,279 input/output pairs. Each pair consisted of an underlying and a surface pronunciation of an individual word of English. The underlying string of each pair was taken from the phoneme-based CMU pronunciation dictionary. The surface string was generated from each underlying form by mechanically applying the one or more rules we were attempting to induce in each experiment. null In our first experiment, we applied the flapping rule in (2) to training corpora of between 6250 and 50,000 words. Figure 11 shows the transducer induced from  glish Flapping As can be seen from Figure 12, the use of alignment information in creating the initial tree transducer dramatically decreases the number of states in the learned transducer as well as the error performance on test data. The improved algorithm induced a flapping transducer with the minimum number of states with as few as 6250 samples. The use of alignment information also reduced the learning time; the additional cost of calculating alignments is more than compensated for by quicker merging of states.</Paragraph>
    <Paragraph position="1"> The algorithm also successfully induced transducers with the minimum number of states for the t-insertion and t-deletion rules below, given only 6250 samples.</Paragraph>
    <Paragraph position="2"> In our second experiment, we applied our learning algorithm to a more difficult problem: inducing multiple rules at once. A data set was constructed by applying the t-insertion rule in (3), the t-deletion rule in (4) and the flapping rule already seen in (2) one after another. As is seen in Figure 13, a transducer of minimum size (five states) was obtained with 12500 or more sample transductions.</Paragraph>
    <Paragraph position="3">  (3) 0 ---, t/n s (4) t---,O/n \[+vocalic\] -stress  The effects of adding decision tress at each state of the machine for the composition of t-insertion, t-deletion and flapping are shown in Figure 14.</Paragraph>
    <Section position="1" start_page="13" end_page="13" type="sub_section">
      <SectionTitle>
Samples
</SectionTitle>
      <Paragraph position="0"> An examination of the few errors (three samples) in the induced flapping and three-rule transducers points out a flaw in our model. While the learned transducer correctly makes the generalization that flapping occurs after any stressed vowel, it does not flap after two stressed vowels in a row. This is possible because no samples containing two stressed vowels in a row (or separated by an 'r') immediately followed by a flap were in the training data. This transducer will flap a 't' after any odd number of stressed vowels, rather than simply after any stressed vowel. Such a rule seems quite unnatural phonologically, and makes for an odd context-sensitive rewrite rule. Any sort of simplest hypothesis criterion applied to a system of rewrite rules would prefer a rule such as --+ V -+ v which is the equivalent of the transducer learned from the training data. This suggests that, the traditional formalism of context-sensitive rewrite rules contains implicit generalizations about how phonological rules usually work that are not present in the transducer system. We hope that further experimentation will lead to a way of expressing this language bias in our induction system.</Paragraph>
    </Section>
  </Section>
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