The system reuses standard techniques for building projective trees by combining adjacent nodes (representing subtrees with adjacent yields), but adds a simple mechanism for swapping the order of nodes on the stack, which gives a system that is sound and complete for the set of all dependency trees over a given label set but behaves exactly like the standard system for the subset of projective trees.
we have presented a novel transition system for dependency parsing that can handle unrestricted non-projective trees.