(2013) show that allowing some degree of non-monotonicity, by using a limited set of non-monotonic actions that can repair past mistakes and replace previously-built arcs, can increase the accuracy of a transition-based parser.
they present a modified arc-eager transition system where the Left-Arc and Reduce transitions are non-monotonic: the former is used to repair invalid attachments made in previous states by replacing them with a leftward arc, and the latter allows the parser to link two words with a rightward arc that were previously left unattached due to an erroneous decision.