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<Paper uid="P98-2192">
  <Title>Restrictions on Tree Adjoining Languages</Title>
  <Section position="7" start_page="1180" end_page="1181" type="concl">
    <SectionTitle>
5 Concluding remarks
</SectionTitle>
    <Paragraph position="0"> Our proposal is intended to contribute to the assessment of the computational complexity of syntactic processing. We have introduced a strict subclass of TAGs having the generative power that is needed to account for the syntactic constructions of natural language that unrestricted TAGs can handle. We have specified a method that recognizes the generated languages in worst case time O(nS), where n is the length of the input string. In order to account for the dependency on the input grammar G, let us define IGI = EN(I + \[Adj(N)1), where N ranges over the set of all nodes of the elementary trees.</Paragraph>
    <Paragraph position="1">  It is not difficult to see that the running time of our method is proportional to I GI.</Paragraph>
    <Paragraph position="2"> Our method works as a recognizer. As for many other tabular methods for TAG recognition, we can devise simple procedures in order to obtain a derived tree associated with an accepted string. To this end, we must be able to 'interleave' adjunctions of left and right trees, that are always kept separate by our recognizer.</Paragraph>
    <Paragraph position="3"> The average case time complexity of our method should surpass its worst case time performance, as is the case for many other tabular algorithms for TAG recognition. In a more applicative perspective, then, the question arises of whether there is any gain in using an algorithm that is unable to recognize more than one wrapping adjunction at each spine, as opposed to using an unrestricted TAG algorithm. As we have tried to argue in Section 4, it seems that standard syntactic constructions do not exploit multiple wrapping adjunctions at a single spine. Nevertheless, the local ambiguity of natural language, as well as cases of ill-formed input, could always produce cases in which such expensive analyses are attempted by an unrestricted algorithm. In this perspective, then, we conjecture that having the single-wrappingadjunction restriction embedded into the recognizer would improve processing efficiency in the average case. Of course, more experimental work would be needed in order to evaluate such a conjecture, which we leave for future work.</Paragraph>
  </Section>
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