A novel approach to Real-time contract based reasoning for Hybrid Systems

Worst Case Execution Time (WCET) analysis of large and complex hybrid systems can be time consuming. Contract based design allows for compositional reasoning of complex systems. Contracts justify the behavior of a system by way of assumptions (which are to be satisfied by the system environment) and guarantees, which are to be met by the system. Contracts also play a major role in compositional reasoning, refinement and re-usability of the system components. In this paper, we present a formal framework to enforce real-time contracts using Hoare triples, for synchronous system design and verification. In that regard, we propose real-time Hoare rules which are based on the WCET of the system and its components. We verify the real-time behavior of the system by applying these rules. These rules not only justify the system behavior and the behavior of its components but their timing as well. We also show that these Hoare rules are sound. Then we show that the synchronous composition of component level Hoare rules based contracts justify a system level contract. This real-time contract composition and reasoning technique which is based on real-time Hoare logic rules is the first ever attempt in synchronous system design and verification.