w n at position i is defined as the set of all paths in the lattice that may be obtained by editing w i : deleting it, substituting it, or inserting a word to its left.
it is the "distance-1-at-position i" neighborhood of w. Given a position i in a word sequence w, all hypotheses in N (w, i) are rescored using the longspan model and the hypothesisŵ (i) with the highest score becomes the new w. The process is repeated with a new position -scanned left to right -until w =ŵ (1) = .