Finding the most probable string and the consensus string: an algorithmic study

Abstract

The problem of finding the most probable string for a distribution generated by a weighted finite automaton is related to a number of important questions: computing the distance between two distributions or finding the best translation (the most probable one) given a probabilistic finite state transducer. The problem is undecidable with general weights and is $\NP$-hard if the automaton is probabilistic. In this paper we give a pseudo-polynomial algorithm which computes the most probable string in time polynomial in the inverse of the probability of this string itself. We also give a randomised algorithm solving the same problem and discuss the case where the distribution is generated by other types of machines.