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<Paper uid="W06-1504">
  <Title>The weak generative capacity of linear tree-adjoining grammars</Title>
  <Section position="5" start_page="31" end_page="31" type="concl">
    <SectionTitle>
4 Conclusion
</SectionTitle>
    <Paragraph position="0"> The weak equivalence of the previously proposed ESL-TAG and SSL-TAG, along with the fact that SL-TAG with substitution and ESL-TAG with substitution belong to the same class, suggests that they represent a useful compromise between CFGs and TAGs. In the two-dimensional language hierarchy of Rambow and Satta (1999), where the two dimensions are rank (how many substructures does a rule combine) and fanout (how many discontinuous spans of the input does a substructure cover), CFGs comprise the fanout-1 grammars and TAGs are a subset of the the fanout-2 grammars; both have arbitrary rank, whereas linear CFGs and linear TAGs are rank-1. The grammars discussed here are mixed: a rule can combine one fanout-2 substructure and an arbitrary number of fanout-1 substructures. A related example would be a version of synchronous CFG that allows only one pair of linked nonterminals and any number of unlinked nonterminals, which could be bitextparsed in O(n5) time, whereas inversion transduction grammar (Wu, 1997) takes O(n6). It may be of interest to make a more general exploration of other formalisms that are mixed in this sense.</Paragraph>
  </Section>
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