Branching bisimulation congruence for probabilistic systems

A notion of branching bisimilarity for the alternating model of probabilistic systems, compatible with parallel composition, is defined. For a congruence result, an internal transition immediately followed by a non-trivial probability distribution is not considered inert. A weaker definition of branching bisimilarity for the same model has been given earlier. Here we show that our branching bisimulation is the coarsest congruence for parallel composition that is included in the weaker version. To support the use of the present equivalence as a reduction technique, we also show that probabilistic CTL formulae are preserved by our equivalence, and we provide a polynomial-time algorithm deciding branching bisimilarity.