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<Paper uid="W94-0204">
  <Title>E DEFAULT FINITE STATE MACHINES AND FINITE STATE PHONOLOGY</Title>
  <Section position="11" start_page="40" end_page="40" type="concl">
    <SectionTitle>
CONCLUSION
</SectionTitle>
    <Paragraph position="0"> We claimed that DFSM's provide an approach to rules that is likely to seem more natural and intuitive to phonologists. Bridging the gap between linguistically adequate formalisms and computationally useful formalisms is a long-term, community effort, and we feel that it would be premature to make claims about the linguistic adequacy of the approach; this depends on whether two-level approaches can be developed and deployed in a way that will satisfy the theoretical and explanatory needs of linguists. A specific claim on which our formalism depends is that all natural two-level phonologies can be reproduced using DFSM's with finitely encodable rules. We feel that this claim is plausible, but it needs to be tested in practice.</Paragraph>
    <Paragraph position="1"> Computationally, our complexity work so far on DFSM's does not preclude the possibility that compilers for generation and recognition (without nulls) exist which will allow for polynomial-time behavior at run-time. Although this question must eventually be resolved, we feel that any implementation is likely to be simpler than that required for KIMMO, and that even a direct implementation of DFSM's can prove adequate in many circumstances. We have not constructed an implementation as yet.</Paragraph>
    <Paragraph position="2"> Like other two-level approaches, we have a problem with surface nulls. It is possible in most realistic recognition applications to bound the number of nulls by some function on the length of the overt input; and it remains to be seen whether a reasonable bound could sufficiently improve complexity in these cases.</Paragraph>
    <Paragraph position="3"> We have dealt with the problem of underlying nulls by simply ruling them out. This simplifies the formal situation considerably, but we do not believe that it is acceptable as a general solution; for instance, we can't expect all cases ofepentheses to occur at morpheme boundaries. If underlying nulls are allowed, though, we will somehow need to limit the places where underlying nulls can occur; this is another good reason to pay attention to a phonotactic level of analysis.</Paragraph>
    <Paragraph position="4"> 9Garey and Johnson, (1979), p. 271.</Paragraph>
  </Section>
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