The key ideas are new feature templates that facilitate state merging of dynamic programming and A* search.
for example, if we lexicalize this model by adding features that depend on the head indices of s 0 and/or s 1 , it increases to O(n 6 • |G| • |N |) since we have to maintain three head indices of A, B, and C. This is why Sagae and Lavie's features are too expensive for our system; they rely on head indices of s 0 , s 1 , s 2 , s 3 , the left and right children of s 0 and s 1 , and so on, leading prohibitively huge complexity.