Reasoning About Real-Time Systems in Event-B Models with Fairness Assumptions

Abstract

Stepwise development supported by the Event-B formalism has been used in the domain of system design and verification. This refinement approach guarantees that safety properties are preserved, while additional reasoning is required to prove the preservation of liveness properties. Our previous work proposes to use real-time trigger-response properties to reason about liveness properties and timed properties in real-time systems. Conditions such as weak fairness assumptions, relative deadlock freedom, and conditional convergence are explored to eliminate Zeno behavior when modeling real-time systems. In this reasoning framework, some strong constraints do not apply to real-world cases. This paper extends our previous results by using strong fairness assumptions to relax these constraints. We present the proof obligations together with temporal properties to construct the theorems and proofs. Fairness assumptions are used to enforce real-time properties in Event-B models. The carrier-sense multiple access with collision detection protocol is used as a case study to illustrate the approach.