N-best search algorithm is very similar to the time synchronous Viterbi search . Since the purpose of the N-best method is to find the optimum speech unit sequence instead of the optimum state sequence, a summing operation should be done instead of the maximum finding operation. However if we completely drop the maximum finding operation it will become the Forward algorithm, and we go back again to the start. Therefore a pruning is performed at every state, (in addition to the pruning of the beam) keeping only the first N paths with the highest scores. Therefore even this algorithm does not give the theoretically optimum sentence. At the end, the algorithm gives N most likely sentences, and for a simple task without post processors ,N=1 is enough .