Both string-toconstituency system (e.g., (Galley et al., 2006;) and string-to-dependency model (Shen et al., 2008) have achieved significant improvements over the state-of-the-art formally syntax-based system Hiero (Chiang, 2007).
those systems also have some limitations that they run slowly (in cubic time) , and do not utilize the useful syntactic information on the source side.