First, there seem to be qualitative constraints on the relationship between the dependency structure of the words in a sentence and their linear ordering.
this relationship seems to be such that any natural language sentence, together with its dependency structure, should be generable by a mildly context-sensitivity formalism (Joshi, 1985), in particular a linear context-free rewrite system in which the right-hand side of each rule has a distinguished head (Pollard, 1984;Vijay-Shanker et al., 1987;Kuhlmann, 2007).