Thus the input i is composed with Map, which is then composed with D, which is composed with the output o. Analogously to the induction of number name grammars described above, since we wish to extract the best alignment leading to the best rule from the instance in question, we compute the shortest path P that lies in the intersection of the output of Map and the input of D, but here we need to preserve the input side as well, since what we need in this case is to learn a transducer that maps between the markup and sequences of tagged spans, and so we do not want to project to the output of i•Map.
: Because of the large number of entities that need to be remembered by the PDT, the approach is not practical in this case.