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<Paper uid="P02-1007">
  <Title>OT Syntax: Decidability of Generation-based Optimizationa0</Title>
  <Section position="9" start_page="0" end_page="0" type="concl">
    <SectionTitle>
9 Conclusion
</SectionTitle>
    <Paragraph position="0"> We showed that for OT-LFG systems in which all constraints can be expressed relative to a local sub-tree in c-structure, the generation task from (noncyclic13) f-structures is solvable. The infinity of 13The non-cyclicity condition is inherited from K&amp;W00; in linguistically motivated applications of the LFG formalism, cruthe conceptually underlying candidate set does not preclude a computational approach. It is obvious that the construction proposed here has the purpose of bringing out the principled computability, rather than suggesting a particular algorithm for implementation. However on this basis, an implementation can be easily devised.</Paragraph>
    <Paragraph position="1"> The locality condition on constraint-checking seems unproblematic for linguistically relevant constraints, since a GPSG-style slash mechanism permits reference to (finitely many) nonlocal configurations from any given category (cf. fn. 5).14 Decidability of generation-based optimization (from a given input f-structure) alone does not imply that the recognition and parsing tasks for an OT grammar system defined as in sec. 3 are decidable: for these tasks, a string is given and it has to be shown that the string is optimal for some underlying input f-structure (cf. (Johnson, 1998)). However, a similar construction as the one presented here can be devised for parsing-based optimization (even for an LFG-style grammar that does not obey the offline parsability condition). So, if the language generated by an OT system is defined based on (strong) bidirectional optimality (Kuhn, 2001, ch. 5), decidability of both the general parsing and generation problem follows.15 For the unidirectionally defined OT language (as in sec. 3), decidability of parsing can be guaranteed under the assumption of a contextual recoverability condition in parsing (Kuhn, in preparation). null cial use of cyclicity in underlying semantic feature graphs has never been made.</Paragraph>
    <Paragraph position="2"> 14A hypothetical constraint that is excluded would be a parallelism constraint comparing two subtree structures of arbitrary depth. Such a constraint seems unnatural in a model of grammaticality. Parallelism of conjuncts does play a role in models of human parsing preferences; however, here it seems reasonable to assume an upper bound on the depth of parallel structures to be compared (due to memory restrictions).</Paragraph>
    <Paragraph position="3"> 15Parsing: for a given string, parsing-based optimization is used to determine the optimal underlying f-structure; then generation-based optimization is used to check whether the original string comes out optimal in this direction too. Generation is symmetrical, starting with an f-structure.</Paragraph>
  </Section>
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