Given input sequence X, the goal of statistical machine translation is to find the best output sequence, Y , that maximizes conditional probability P (Y |X): The problem of sentence boundary detection can be reduced to the problem of translating a sequence of words, X, that does not include periods but instead includes pauses into a sequence of words, Y , that includes periods.
in places where a pause might be converted into a period, which means P (X|Y ) = 1, the decision whether a period should be inserted or not is made by comparing language model scores P (Y ) and P (Y ).