If the rule r has n variables and each variable consists of 1 elements then the complexity is n x / 2 , while the recursive way be l n In addtion, each rule ri can be assigned a translation score as the value of the formular (3) and output translations for the input sentence can be sorted according to the score value on the whole of rules in template rules.
our method using HMM modeling can be avoided the exponential calculation problem by using the dynamic algorithm.