Abstract
The paper formulates the Hays and Gaifman dependency grammar (HGDG) in terms of constraints on a string based encoding of dependency trees and develops an approach to obtain a regular approximation for these grammars. Our encoding of dependency trees uses brackets in a novel fashion: pairs of brackets indicate dependencies between pairs of positions rather than boundaries of phrases. This leads to several advantages: (i) HGDG rules over the balanced bracketing can be expressed using regular languages. (ii) A new homomorphic representation for context-free languages is obtained. (iii) A star-free regular approximation for the original projective dependency grammar is obtained by limiting the number of stacked dependencies. (iv) By relaxing certain constraints, the encoding can be extended to non-projective dependency trees and graphs, (v) strong generative power of HGDGs can now be characterized through sets of bracketed strings.
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