Deciding Bisimilarity and Similarity for Probabilistic Processes

摘要

This paper deals with probabilistic and nondeterministic processes represented by a variant of labeled transition systems where any outgoing transition of a state s is augmented with probabilities for the possible successor states. Our main contributions are algorithms for computing this bisimulation equivalence classes as introduced by Larsen and Skou (1996, Inform. and Comput.99, 1–28), and the simulation preorder à la Segala and Lynch (1995, Nordic J. Comput.2, 250–273). The algorithm for deciding bisimilarity is based on a variant of the traditional partitioning technique and runs in time O(mn(log m+log n)) 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 flow problems in suitable networks. Using the method of Cheriyan, Hagerup, and Mehlhorn, (1990, Lecture Notes in Computer Science, Vol. 443, pp. 235–248, Springer-Verlag, Berlin) for computing the maximum flow, 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 Jonsson and Larsen (1991, “Proc. LICS'91” pp. 266–277) in fully probabilistic systems (a variant of ordinary labeled transition systems where the nondeterminism is totally resolved by probabilistic choices).