Deciding Bisimilarity and Similarity for Probabilistic Processes

This paper deals with probabilistic and nondeterministic processes represented by a variant of labelled transition systems where any outgoing transition of a state s is augmented with probabilities for the possible successor states. Our main contribution are algorithms for computing the bisimulation equivalence classes as introduced by Larsen & Skou [44] and the simulation preorder a la Segala & Lynch [57]. The algorithm for deciding bisimilarity is based on a variant of the traditional partitioning technique [43, 51] and runs in time O(mn(logm+ logn)) where m is the number of transitions and n the number of states. The main idea for computing the simulation preorder is the reduction to maximum ow problems in suitable networks. Using the method of Cheriyan, Hagerup & Mehlhorn [15] for computing the maximum ow, the algorithm runs in time O((mn6 +m2n3)= log n). Moreover, we show that the network-based technique is also applicable to compute the simulation-like relation of [40] in fully probabilistic systems (a variant of ordinary labelled transition systems where the non-determinism is totally resolved by probabilistic choices).