On Probabilistic Automata in Continuous Time

Abstract

We develop a compositional behavioural model that integrates a variation of probabilistic automata into a conservative extension of interactive Markov chains. The model is rich enough to embody the semantics of generalised stochastic Petri nets. We define strong and weak bisimulations and discuss their compositionality properties. Weak bisimulation is partly oblivious to the probabilistic branching structure, in order to reflect some natural equalities in this spectrum of models. As a result, the standard way to associate a stochastic process to a generalised stochastic Petri net can be proven sound with respect to weak bisimulation.