Branching Bisimulation Congruence for Probabilistic Systems

The notion of branching bisimulation for the alternating model of probabilistic systems is not a congruence with respect to parallel composition. In this paper we first define another branching bisimulation in the more general model allowing consecutive probabilistic transitions, and we prove that it is compatible with parallel composition. We then show that our bisimulation is actually the coarsest congruence relation included in the existing branching bisimulation when restricted to the alternating model.