Numerically Representing Stochastic Process Algebra Models
Stochastic process algebras combine a high-level system description in terms of interacting components, with a rigorous low-level mathematical model in terms of a stochastic process. These have proved to be valuable modelling formalisms, particularly in the areas of performance modelling and systems biology. However, they do suffer from the problem of state space explosion. Currently, the underlying stochastic process is generally derived via the small step operational semantics of the process algebra and relies on a syntactical representation of the states of the process. In this paper, we propose a numerical representation schema based on a counting abstraction. This automatically detects symmetries within the state space based on replicated components, and produces a compact state space. Moreover, as we demonstrate, it is amenable to other interpretations and thus other forms of computational analysis, enriching the set of qualitative and quantitative measures that can be derived from a model.
stochastic process algebra numerical representation state space representation compact state representation pepa