 
Summary: Dependency Grammars and ContextFree Grammars
Steven Abney
University of Tšubingen
The question arises from time to time what the relation is between depen
dency grammars (DG's) and phrasestructure grammars. A classic paper by
Gaifman [1] would appear to have laid the issue to rest, by proving that depen
dency grammars are a special case of contextfree grammars (CFG's). Gaifman
proves that dependency grammars are equivalent to a proper subset of phrase
structure grammars, those of degree 1, which I will dub d1CFG's. (As degree
cannot be explained in a few words, I will leave it undefined for the moment.)
Under a weaker notion of correspondence, which Gaifman attributes to Hays
[2], dependency grammars correspond to finitedegree CFG's, which represent
a larger subset of CFG's, but a proper subset nonetheless.
I submit, however, that Gaifman correlates DG's with a proper subset of
CFG's only by suppressing the essential property of DG's, namely, their head
edness. I would like to show that, if we take headedness seriously, we are led
to the conclusion that DG's and CFG's both represent equivalence classes of
what I will call headed contextfree grammars (HCFG's), but that neither DG's
nor CFG's subsume the other. Nonetheless, Gaifman's result is preserved in
a different form, in that the equivalence classes defined by CFG's include all
