Each path from q I to a final state q F has • an input string x, given by the concatenation of its arcs' input labels; • an output string y, given similarly; • a probability, given by the product of its arcs' probabilities and the halt probability of q F .
log p θ (y k | x k ) depends only on the probabilities of edit arcs in T that appear in x k • T • y k , and the competing edit arcs from the same edit states q C .