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<Paper uid="P97-1043">
  <Title>The Complexity of Recognition of Linguistically Adequate Dependency Grammars</Title>
  <Section position="8" start_page="341" end_page="342" type="concl">
    <SectionTitle>
5 Conclusion
</SectionTitle>
    <Paragraph position="0"> We have shown that current DG theorizing exhibits a feature not contained in previous formal studies of DG, namely the independent specification of dominance and precedence constraints. This feature leads to a A/'7% complete recognition problem. The necessity of this extension approved by most current DGs relates to the fact that DG must directly characterize dependencies which in PSG are captured by a projective structure and additional processes such as coindexing or structure sharing (most easily seen in treatments of so-called unbounded  dependencies). The dissociation of tree structure and linear order, as we have done in Section 3, nevertheless seems to be a promising approach for PSG as well; see a very similar proposal for HPSG (Reape, 1989).</Paragraph>
    <Paragraph position="1"> The .N'79-completeness result also holds for the discontinuous DG presented in Section 3. This DG can characterize at least some context-sensitive languages such as anbnc n, i.e., the increase in complexity corresponds to an increase of generative capacity. We conjecture that, provided a proper formalization of the other DG versions presented in Section 2, their .A/P-completeness can be similarly shown. With respect to parser design, this result implies that the well known polynomial time complexity of chart- or tabular-based parsing techniques cannot be achieved for these DG formalisms in general. This is the reason why the PARSETALK text understanding system (Neuhaus &amp; Hahn, 1996) utilizes special heuristics in a heterogeneous chart- and backtracking-based parsing approach.</Paragraph>
  </Section>
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