Exploring probabilistic bisimulations

We take a fresh look at strong probabilistic bisimulations for processes which exhibit both non-deterministic and probabilistic behaviour. We suggest that it is natural to interpret such processes as distributions over states in a probabilistic labelled transition system, a pLTS; this enables us to adapt the standard notion of contextual equivalence to this setting. We then prove that a novel form of bisimulation equivalence between distributions are both sound and complete with respect to this contextual equivalence. We also show that a very simple extension to HML, Hennessy-Milner Logic, provides finite explanations for inequivalences between distributions. Finally we show that our bisimulations between distributions in a pLTS are simply an alternative characterisation of a standard notion of probabilistic bisimulation equivalence, defined between states in a pLTS.