We say that a complete non-deterministic oracle is correct if and only if, for every projective dependency tree T with yield W , every configuration c that is reachable from INITIAL(W ), and every transition t ∈ o d (c, T ), min A:c;A C(A, T ) = min A:t(c);A C(A, T ), where c ; A signifies that the parse A is reachable from c, a notion that will be formally defined in the next subsection.
even if the gold tree T is no longer reachable itself, the best tree reachable from t(c) has the same cost as the best tree reachable from c. In addition to a cost function for arc sets and trees, it is convenient to define a cost function for transitions.