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<Paper uid="P97-1043">
  <Title>The Complexity of Recognition of Linguistically Adequate Dependency Grammars</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> The introduction of dependency grammar (DG) into modern linguistics is marked by Tesni~re (1959). His conception addressed didactic goals and, thus, did not aim at formal precision, but rather at an intuitive understanding of semantically motivated dependency relations. An early formalization was given by Gaifman (1965), who showed the generative capacity of DG to be (weakly) equivalent to standard context-free grammars.</Paragraph>
    <Paragraph position="1"> Given this equivalence, interest in DG as a linguistic framework diminished considerably, although many dependency grammarians view Gaifman's conception as an unfortunate one (cf. Section 2). To our knowledge, there has been no other formal study of DG.This is reflected by a recent study (Lombardo &amp; Lesmo, 1996), which applies the Earley parsing technique (Earley, 1970) to DG, and thereby achieves cubic time complexity for the analysis of DG. In their discussion, Lombardo &amp; Lesmo express their hope that slight increases in generative capacity will correspond to equally slight increases in computational complexity. It is this claim that we challenge here.</Paragraph>
    <Paragraph position="2"> After motivating non-projective analyses for DG, we investigate various variants of DG and identify the separation of dominance and precedence as a major part of current DG theorizing. Thus, no current variant of DG (not even Tesni~re's original formulation) is compatible with Gaifman' s conception, which seems to be motivated by formal considerations only (viz., the proof of equivalence). Section 3 advances our proposal, which cleanly separates dominance and precedence relations. This is illustrated in the fourth section, where we give a simple encoding of an A/P-complete problem in a discontinuous DG. Our proof of A/79-completeness, however, does not rely on discontinuity, but only requires unordered trees.</Paragraph>
    <Paragraph position="3"> It is adapted from a similar proof for unordered context-free grammars (UCFGs) by Barton (1985).</Paragraph>
  </Section>
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