 Because of their greater expressiveness, TAGs and CCGs are harder to parse in the worst case (O(n6)) than CFGs and projective DGs (O(n3)), at least with current algorithms (see Vijay-Shankar &amp; Weir 1994 for parsing algorithms for TAG, CCG, and  LIG based on bottom-up dynamic programming). However, it does not follow that TAG parsing or CCG parsing is impractical for real grammars and real language, and in fact parsers exist for both that are competitive with more common CFG-based parsers.  