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LOOP. until <math>t(e_x | f_y)</math> converges:<blockquote><math>t(e_x | f_y) \leftarrow \frac{t(e_x|f_y)}{\lambda_y} \sum_{k, i, j}\frac{\delta(e_x, e_i^{(k)})\delta(f_y, f_{j}^{(k)})}{\sum_{j'}t(e_i^{(k)}|f_{j'}^{(k)})}</math>
<blockquote>where each <math>\lambda_y</math> is a normalization constant that makes sure each <math>\sum_x t(e_x|f_y) = 1</math>.</blockquote></blockquote>RETURN. <math>t(e_x | f_y)</math>.</blockquote>In the above formula, <math>\delta</math> is the [[Dirac delta function]] -- it equals 1 if the two entries are equal, and 0 otherwise. The index notation is as follows:<blockquote><math>k</math> ranges over English-foreign sentence pairs in corpus;
<math>i</math> ranges over words in English sentences;
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