A POLYNOMIAL-TIME ALGORITHM FOR THE EQUIVALENCE OF PROBABILISTIC-AUTOMATA

Two probabilistic automata are equivalent if for any string x, the two automata accept x with equal probability. This paper presents an O((n1 + n2)4) algorithm for determining whether two probabilistic automata U1 and U2 are equivalent, where n1 and n2 are the number of states in U1 and U2, respectively. This improves the best previous result, which showed that the problem was in coNP. The existence of this algorithm implies that the covering and equivalence problems for uninitiated probabilistic automata are also polynomial-time solvable. The algorithm used to determine the equivalence of probabilistic automata can also solve the path equivalence problem for nondeterministic finite automata without lambda-transitions and the equivalence problem for unambiguous finite automata in polynomial time. This paper studies the approximate equivalence (or delta-equivalence) problem for probabilistic automata. An algorithm for the approximate equivalence problem for positive probabilistic automata is given.