Like ordinary outside costs, bridge outside costs form consistent and admissible estimates of the true Viterbi outside score α(e) of an edge e. Because bridge costs mix rules from the finer and coarser grammar, bridge costs are at least as good an estimate of the true outside score as entirely coarse outside costs, and will in general be much tighter.
that is, we have α(e ) ≤α(e) ≤ α(e) note that the bridge costs become better approximations farther right in the sentence, and the bridge cost of the last word in the sentence is equal to the Viterbi outside cost of that word.