On the one hand, this can be used as an analytical tool to characterize existing systems for dependency parsing and prove formal properties related to expressivity and complexity.
we have shown that all divisible systems, including a number of well-known systems from the literature, are sound for planar dependency graphs and can be restricted to satisfy a number of other formal constraints, and we have characterized the subclass of efficient divisible transition systems that give linear parsing complexity when combined with greedy inference or beam search as is customary in transition-based parsing.