Reduction Semantics in Markovian Process Algebra

Stochastic (Markovian) process algebra extend classical process algebra with probabilistic exponentially distributed time durations denoted by rates (the parameter of the exponential distribution). Defining a semantics for such an algebra, so to derive Continuous Time Markov Chains from system specifications, requires dealing with transitions labeled by rates. With respect to standard process algebra semantics this poses a problem: we have to take into account the multiplicity of several identical transitions (with the same rate). Several techniques addressing this problem have been introduced in the literature, but they can only be used for semantic definitions that do not exploit a structural congruence relation on terms while inferring transitions. On the other hand, using a structural congruence relation is a useful mechanism that is commonly adopted, for instance, in order to define semantics in reduction style for non-basic process algebras such as the pi-calculus or richer ones. In this paper we show how to define semantics for Markovian process algebra when structural congruence is used while inferring transitions and, as an application example, we define the reduction semantics for a stochastic version of the pi-calculus. Moreover we show such semantics to be correct with respect to the standard one (defined in labeled operational semantics style).