Why can the Viterbi algorithm guarantee the optimal solution?
It is because of the Generalized Distributive Law.
How can Viterbi become Beam Search?
Source: NLP Programming Tutorial 13 - Beam and A* Search by professor Graham Neubig
Then the reverse is the process to convert beam search into Viterbi. Because in Beam Search some unpromising parts of search space are pruned, and then we cannot apply the Generalized Distributive Law, and hence it can not guarantee an optimal path.