Computing the Most Probable String with a Probabilistic Finite State Machine

The problem of finding the consensus / most probable string for a distribution generated by a probabilistic finite automaton or a hidden Markov model arises in a number of natural language processing tasks: it has to be solved in several transducer related tasks like optimal decoding in speech, or finding the most probable translation of an input sentence. We provide an algorithm which solves these problems in time polynomial in the inverse of the probability of the most probable string, which in practise makes the computation tractable in many cases. We also show that this exact computation compares favourably with the traditional Viterbi computation.