The string-to-tree decoder searches for the optimal derivation d * that parses a Japanese string F into a packed forest of the set of all possible derivations D: This formula differs from Equation 2 by replacing E t with F in s(d|•) and adding g (d), which is the number of glue rules used in d. Further definitions of s(d|F ) and f (r) are identical with those used in Equation 2.
we use a CKY-style algorithm with beam-pruning and cube-pruning (Chiang, 2007) to decode Japanese sentences.