Kuhlmann (2007) investigates several such classes, based on well-nestedness and gap degree constraints (Bodirsky et al., 2005), relating them to lexicalised constituency grammar formalisms.
he shows that: linear context-free rewriting systems (LCFRS) with fan-out k (Vijay-Shanker et al., 1987;Satta, 1992) induce the set of dependency structures with gap degree at most k − 1; coupled context-free grammars in which the maximal rank of a nonterminal is k (Hotz and Pitsch, 1996) induce the set of well-nested dependency structures with gap degree at most k − 1; and LTAGs (Joshi and Schabes, 1997) induce the set of well-nested dependency structures with gap degree at most 1.