Stochastic Pi-calculus Revisited

We develop a version of stochastic Pi-calculus endowed with a structural operational semantics expressed in terms of measure theory. The paper relies on two observations: (i) the structural congruence organizes a measurable space of processes and (ii) a well behaved SOS associates to each process, in a specified rate environment, a behaviour defined by a set of measures over the measurable space of processes. The measures, indexed with observable actions, encode the rates of the transitions from a process (state of a system) to a measurable set of processes. We extend the notion of stochastic bisimulation to include the concept of rate environment and prove that this equivalence is a congruence which extends the structural congruence.