Compositional Representation and Reduction of Stochastic Labelled Transition Systems based on Decision Node BDDs

Compact symbolic representations of large labelled transition systems, based on binary decision diagrams (BDD), are discussed. Extensions of BDDs are considered, in order to represent stochastic transition systems for performability analysis. We introduce Decision Node BDDs, a novel stochastic extension of BDDs which preserves the structure and properties of purely functional BDDs. It is shown how parallel composition of components can be performed in this context, without leading to state space explosion. Furthermore, we discuss state space reduction by Markovian bisimulation, also entirely based on symbolic techniques. Together, parallel composition and state space reduction enable a compositional approach to the stochastic modelling of concurrent systems.