, b k be the set of words that align to a in the aligned sentence t. In general, we can consider U a = {U a,s→t } s∈Da to be the candidate set of translations for a in T , where D a is the set of source language sentences containing a.
this definition is quite noisy: a word b i might have been aligned with a arbitrarily; or, b i might be a word that itself corresponds to a multiword translation in S. Thus, we also align the sentences in the T → S direction, and require that each b i in the phrase aligns either with a or with nothing.