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<Paper uid="P99-1070">
  <Title>Relating Probabilistic Grammars and Automata</Title>
  <Section position="9" start_page="548" end_page="548" type="concl">
    <SectionTitle>
8 Conclusions
</SectionTitle>
    <Paragraph position="0"> The relationship between PCFGs and PPDAs is subtler than a direct application of the classical constructions relating general CFGs and PDAs. Although PCFGs can be concisely translated into top-down PPDAs, we conjecture that there is no concise translation of PCFGs into shift-reduce PPDAs. Conversely, there appears to be no concise translation of shift-reduce PPDAs to PCFGs. Our main result is that PCFGs and shift-reduce PPDAs are intertranslatable, hence weakly equivalent. However, the nonconciseness of our translations is consistent with the view that stochastic top-down generation models are significantly different from shift-reduce stochastic parsing models, affecting the ability to learn a model from examples.</Paragraph>
  </Section>
class="xml-element"></Paper>