, m} as follows: ψ(i) is the set of source positions which are mapped to the target location i by the alignmentã and the fertility of the target position i We can rewrite each of the IBM models P r (f ,ã|e) as follows: Table 2 shows the breaking of P r (f ,ã|e) into the constituents T i , D i and N i .
we can write P r (f ,ã|e) P r (e) as: where L i = trigram(e i |e i−2 , e i−1 ) and λ is the trigram probability of the boundary word.