They assumed that if two English phrases e 1 and e 2 are aligned with the same phrase c in another language, these two phrases may be paraphrases.
they computed the paraphrase probability in terms of the translation probabilities: are the probabilities of translating e 1 to c and c to e 2 , which are computed based on MLE: where count(c, e 1 ) is the frequency count that phrases c and e 1 are aligned in the corpus.