A Hierarchy of Equivalences for Probabilistic Processes

We study several process equivalences on a probabilistic process algebra. First, we define an operational semantics. Afterwards we introduce the notion of passing a test with a probability. We consider three families of tests according to the intended behavior of an external observer: Reactive (sequential tests), generative (branching tests), and limited generative (equitable branching tests). For each of these families we define three predicates over processes and tests (may-pass, mustpass, passp ) which induce three equivalences. Finally, we relate these nine equivalences and provide either alternative characterizations or fully abstract denotational semantics. These semantic frameworks cover from simple traces to probabilistic acceptance trees.