Computing the prefix of an automaton

We present an algorithm for computing the prefix of an automaton. Automata considered are non-deterministic, labelled on words, and can have epsilon - transitions. The prefix automaton of an automaton A has the following chara cteristic properties. It has the same graph as A. Each accepting path has t he same label as in A. For each state q, the longest common prefix of the l abels of all paths going from q to an initial or final state is empty. The interest of the computation of the prefix of an automaton is that it is the first step of the minimization of sequential transducers. The algorithm th at we describe has the same worst case time complexity as another algorithm due to Mohri but our algorithm allows automata that have empty labelled cy cles. If we denote by P(q) the longest common prefix of labels of paths goi ng from q to an initial or final state, it operates in time O((P + 1) x \E \) where P is the maximal length of all P(q).