More recently, Chiang (2010) has shown that ("exact") tree-to-tree translation as parsing achieves comparable performance with Hiero (Chiang, 2007) using much fewer rules.
given a natural rule the following deductive step grows an item in the chart by the rule where PP 1,3 denotes the recognition of the nonterminal PP spanning from the substring from position 1 through 3 (i.e., yu shalong in Figure 2), w 1 and e 1 are the score and translation of the first antecedent item, respectively, and the resulting item score is calculated as: 5 As the PCFg probabilities of natural rules are fixed during decoding, they can be pre-computed and stored in the rule table.