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<Paper uid="E89-1007">
  <Title>ON THE GENERATIVE POWER OF TWO.LEVEL MORPHOLOGICAL RULES</Title>
  <Section position="12" start_page="0" end_page="0" type="concl">
    <SectionTitle>
CONCLUSIONS
</SectionTitle>
    <Paragraph position="0"> We have presented an alternative formal statement of the meaning of Koskenniemi's notation for two-level morphological rules. This definition appears to be wholly faithful to the original informal explanations of the intent of two-level morphological rules, but is independent of the expression of the rules as transducers. The generative power of two-level morphological grammars, viewed as ways of characterising sets of sequences of symbol-pairs, is less than that of arbitrary transducers, despite the fact that the transducer formulation is sometimes discussed as if it were the essential definition of the two-level model.</Paragraph>
    <Paragraph position="1"> It now remains to determine further properties of the set of two-level generatable languages. Barton et al.(1987) have shown that the recognition problem for two-level transducers (including cross-linked lexicons) is NPcomplete, and a very similar demonstration can be constructed for the two-level model defined here. Closure properties (or lack thereof) of the two-level generatable languages are yet to be proven.</Paragraph>
  </Section>
class="xml-element"></Paper>