Towards Refinement Semantics of Real-Time Trigger-Response Properties in Event-B

Abstraction and refinement offer a stepwise development approach to managing complexity in system design. Based on our previous work that extends Event-B models with high level real-time trigger-response properties, this paper presents refinement semantics of timed systems using behavioral traces. Forward simulation, which is a proof technique for refinement, is used to verify the consistency between different refinement levels. To prove refinement of trace semantics, we construct intermediate traces from concrete traces with a mapping function and prove the intermediate trace without stuttering events and states are abstract traces. Fairness assumptions, relative deadlock freedom, and conditional convergence are adopted in refinement steps to eliminate Zeno behavior in timed models. Based on the semantics, we develop refinement rules and strategies to perform refinement on timed models and refine real-time trigger-response properties into sequential or alternative sub-timing properties with proofs.