Probabilistic Contracts for Component-Based Design

We define a framework of probabilistic contracts for constructing componentbased embedded systems, based on the formalism of discrete-time Interactive Markov Chains. A contract specifies the assumptions a component makes on its context and the guarantees it provides. Probabilistic transitions represent allowed uncertainty in the component behavior, for instance, to model internal choice or reliability. Action transitions are used to model non-deterministic behavior and communication between components. An interaction model specifies how components interact with each other. We provide the ingredients for a component-based design flow, including (1) contract satisfaction and refinement, (2) parallel composition of contracts over disjoint, interacting components, and (3) conjunction of contracts describing different requirements over the same component. Compositional design is enabled by congruence of refinement.