Formal Treatment of Real-time Properties in Event-B

Abstract

Timing and concurrency are two critical properties of Cyber-Physical Systems (CPS). Functional and timing requirements needed to be satisfied in CPS to avoid unsafe situations. Formal methods, which are mathematical techniques for specifying and verifying systems, aid software engineering by ensuring the correctness of the system design.

The Event-B formalism offers a stepwise development approach to manage complexity in system design. Our work provides formal treatment of real-time properties in Event-B models from both the semantics perspective and syntax perspective. There is existing work on treating real-time properties in Event-B but it lacks a semantic treatment in terms of trace behaviors. Because timing properties require fairness assumptions, we use infinite traces and develop conditions under which all infinite traces of a machine satisfy trigger-response and timing properties. We present refinement semantics of models whose behavior traces are infinite. Based on forward simulation, fairness assumptions, relative deadlock freedom, and conditional convergence are adopted as additional conditions that guarantee infinite trace refinement of timed models.

Also, the existing work that extends Event-B models with discrete timing properties inadequately represents the communication and competition between concurrent tasks in concurrent systems. We present the semantics of parameterized real-time trigger-response properties of Event-B models based on timing invariants. We show a method of syntactically encoding parameterized real-time trigger-response properties in Event-B machines. To capture the concurrency between tasks, we distinguish end-to-end timing properties and scheduler-based timing properties from the perspective of different system design phases. We model end-to-end timing properties as parameterized timing properties and scheduler-based timing properties as unparameterized timing properties. A nondeterministic queue-based scheduling framework is proposed to replace end-to-end timing properties with scheduler-based timing properties.

Finally, we demonstrate our approach with three real-time case studies. We show how to treat real-time properties in a stepwise modeling and verification process with Event-B models.

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Identifiers

ORCID for Chenyang Zhu: orcid.org/0000-0002-2145-0559

ORCID for Michael Butler: orcid.org/0000-0003-4642-5373

ORCID for Corina Cirstea: orcid.org/0000-0003-3165-5678

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