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<Paper uid="C04-1011">
  <Title>Kullback-Leibler Distance between Probabilistic Context-Free Grammars and Probabilistic Finite Automata</Title>
  <Section position="8" start_page="0" end_page="0" type="concl">
    <SectionTitle>
7 Conclusions
</SectionTitle>
    <Paragraph position="0"> We have discussed the computation of the KL distance between PCFGs and deterministic PFAs. We have argued that exact computation is di cult in general, but for determining the relative qualities of di erent PFAs, with respect to their closeness to an input PCFG, it su ces to compute the cross-entropy. We have shown that the cross-entropy between a PCFG and a deterministic PFA can be computed exactly.</Paragraph>
    <Paragraph position="1"> These results can also be used for comparing a pair of PFAs, one of which is deterministic.</Paragraph>
    <Paragraph position="2"> Generalization of PCFGs to probabilistic tree-adjoining grammars (PTAGs) is also possible, by means of the intersection of a PTAG and a PFA, along the lines of (Lang, 1994).</Paragraph>
  </Section>
class="xml-element"></Paper>