The particular case a(j) = 0 means that the position j in t is not aligned with any position in s. All the possible alignments between t and s are denoted by A(s, t), and the probability of translating a given s into t by an alignment a is Pr(t, a | s).
an optimal alignment between s and t can be computed aŝ Different approaches for estimating Pr(t, a | s) were proposed in Brown et al.