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<Paper uid="P97-1040">
  <Title>Efficient Generation in Primitive Optimality Theory</Title>
  <Section position="6" start_page="319" end_page="319" type="concl">
    <SectionTitle>
5 Conclusions
</SectionTitle>
    <Paragraph position="0"> Primitive Optimality Theory, or OTP, is an attempt to produce a a simple, rigorous, constraint-based model of phonology that is closely fitted to the needs of working linguists. I believe it is worth study both as a hypothesis about Universal Grammar and as a formal object.</Paragraph>
    <Paragraph position="1"> The present paper introduces the OTP formalization to the computational linguistics community. We have seen two formal results of interest, both having to do with generation of surface forms: * OTP's generative power is low: finite-state optimization. In particular it is more constrained than theories using Generalized Alignment. This is good news for comprehension and learning.</Paragraph>
    <Paragraph position="2"> * OTP's computational complexity, for generation, is nonetheless high: NP-complete on the size of the grammar. This is mildly unfortunate for OTP and for the OT approach in general.</Paragraph>
    <Paragraph position="3"> It remains true that for a fixed grammar, the time to do generation is close to linear on the size of the input (Ellison, 1994), which is heartening if we intend to optimize long utterances with respect to a fixed phonology.</Paragraph>
    <Paragraph position="4"> Finally, we have considered the prospect of building a practical tool to generate optimal outputs from OT theories. We saw above to set up the representations and constraints efficiently using deterministic finite-state automata, and how to remedy some hidden inefficiencies in the seminal work of (Ellison, 1994), achieving at least a 100-fold observed speedup. Delayed intersection and aggressive pruning prove to be important. Aggressive minimization and a more compact. &amp;quot;factored&amp;quot; representation of automata may also turn out to help.</Paragraph>
  </Section>
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