We implemented our algorithms within the Tur-boParser (Martins et al., 2013) 2 .
every other aspect of the parser -feature set, pruning algorithm, cost-augmented MIRA training (Crammer et al., 2006) etc., is kept fixed but our algorithms replace the inference algorithms: Chu-Liu- Edmonds ((Edmonds, 1967), first order) and dual-decomposition (higher order).