Weak bisimulation is sound and complete for pCTL*

Abstract. We investigate weak bisimulation of probabilistic systems in the presence of nondeterminism, i.e. labelled concurrent Markov chains (LCMC) with silent transitions. We build on the work of Philippou, Lee and Sokolsky [1] for £nite state LCMCs. Their de£nition of weak bisimulation destroys the additivity property of the probability distributions, yielding instead capacities. The mathematics behind capacities naturally captures the intuition that when we deal with nondeterminism we must work with estimates on the possible probabilities. Our analysis leads to three new developments: – We identify an axiomatization of “image £niteness” for countable state systems and present a new de£nition of weak bisimulation for these LCMCs. We prove that our de£nition coincides with that of Philippou, Lee and Sokolsky for £nite state systems. – We show that bisimilar states have matching computations. The notion of matching involves linear combinations of transitions. This idea i...

• Type: Journal
• Year: 2010
• Where: IANDC
• Authors: Josée Desharnais, Vineet Gupta, Radha Jagadeesan, Prakash Panangaden
• Keywords: IANDC 2010, State Systems, Weak Bisimulation, £nite State