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Probabilistic bisimulation as a congruence
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ε-bisimulationequivalence has been proposed inthe literature as a technique to study the concept ofbehavioral distancebetween probabilistic processes. Inthis paper we consider also two stronger equivalences:action¿-bisimulation and global¿-bisimulation. For each of these three equivalencenotions we propose an SOS transition rule format ensuring theproperty of non-expansiveness. Non-expansiveness meansthat if the behavioral distance between siand tiisεi, then the behavioraldistance between f(s1,...,sn) and f(t1,...,tn) is no more thatε1+ ... + εn. As expected, the stronger theε-bisimulation considered, the (slightly) weakerthe constraints of the transition rule format.