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<Paper uid="P06-1137">
  <Title>Sydney, July 2006. c(c)2006 Association for Computational Linguistics Highly constrained unification grammars</Title>
  <Section position="7" start_page="1094" end_page="1095" type="concl">
    <SectionTitle>
5 Conclusions
</SectionTitle>
    <Paragraph position="0"> The main contribution of this work is the definition of two constraints on unification grammars which dramatically limit their expressivity. We prove that non-reentrant unification grammars generate exactly the class of context-free languages; and that one-reentrant unification grammars generate exactly the class of mildly context-sensitive languages. We thus obtain two linguistically plausible constrained formalisms whose computational processing is tractable.</Paragraph>
    <Paragraph position="1"> This main result is primarily a formal grammar result. However, we maintain that it can be easily adapted such that its consequences to (practical) computational linguistics are more evident. The motivation behind this observation is that reentrancy only adds to the expressivity of a grammar formalism when it is potentially unbounded, i.e., when infinitely many feature structures can be the possible values at the end of the reentrant paths. It is therefore possible to modestly extend the class of unification grammars which can be shown to generate exactly the class of mildly context-sensitive languages, by allowing also a limited form of multiple reentrancies among the elements in a rule (e.g., to handle agreement phenomena). This can be most useful for grammar writers, and at the same time adds nothing to the expressivity of the formalism. We leave the formal details of such an extension to future work.</Paragraph>
    <Paragraph position="2"> This work can also be extended in other directions. The mapping of one-reentrant UGs to LIG is highly verbose, resulting in LIGs with a huge  number of rules. We believe that it should be possible to optimize the mapping such that much smaller grammars are generated. In particular, we are looking into mappings of one-reentrant UGs to other MCSL formalisms, notably TAG.</Paragraph>
    <Paragraph position="3"> The two constraints on unification grammars (non-reentrant and one-reentrant) are parallel to the first two classes of the Weir (1992) hierarchy of languages. A possible extension of this work could be a definition of constraints on unification grammars that would generate all the classes of the hierarchy. Another direction is an extension of one-reentrant unification grammars, where the reentrancy does not have to be between the head and one element of the body. Also of interest are two-reentrant unification grammars, possibly with limited kinds of reentrancies.</Paragraph>
  </Section>
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