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<Paper uid="P91-1032">
  <Title>NP -+ Det Nom \[ PN Det -+ Art \] NP's Nom -+ N I Nom PP J Adj Nom</Title>
  <Section position="9" start_page="252" end_page="253" type="concl">
    <SectionTitle>
6 Related Work and Conclu-
</SectionTitle>
    <Paragraph position="0"> sions Our work can be seen as an algorithmic realization of suggestions of Church and Patil (1980; 1982) on algebraic simplifications of CFGs of regular languages. Other work on finite state approximations of phrase structure grammars has typically relied on arbitrary depth cutoffs in rule application. While this is reasonable for psycholinguistic modeling of performance restrictions on center embedding (Pulman, 1986), it does not seem appropriate for speech recognition where the approximating FSA is intended to work as a filter and not reject inputs acceptable by the given grammar. For instance, depth cutoffs in the method described by Black (1989) lead to approximating FSAs whose language is neither a subset nor a superset of the language of the given phrase-structure grammar.</Paragraph>
    <Paragraph position="1"> In contrast, our method will produce an exact FSA for many interesting grammars generating regular languages, such as those arising from systematic attachment ambiguities (Church and Patil, 1982).</Paragraph>
    <Paragraph position="2"> It important to note, however, that even when the result FSA accepts the same language, the original grammar is still necessary because interpreta-SWe have already implemented a version of the algorithm that splits the grammar into strongly connected components, approximates and minimizes separately each component and combines the results, but the main purpose of this version is to reduce approximation and determinization costs for some grmmmars.</Paragraph>
    <Paragraph position="3">  tion algorithms are generally expressed in terms of phrase structures described by that grammar, not in terms of the states of the FSA.</Paragraph>
    <Paragraph position="4"> Although the algorithm described here has mostly been adequate for its intended application -- grammars sufficiently complex not to be approximated within reasonable time and space bounds usually yield automata that are far too big for our current real-time speech recognition hardware -- it would be eventually of interest to handle right-recursion in a less profligate way. In a more theoretical vein, it would also be interesting to characterize more tightly the class of exactly approximable grammars. Finally, and most speculatively, one would like to develop useful notions of degree of approximation of a language by a regular language. Formal-language-theoretic notions such as the rational index (Boason et al., 1981) or probabilistic ones (Soule, 1974) might be profitably investigated for this purpose.</Paragraph>
  </Section>
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