Towards the Semi-Automatic Verification of Parameterized Real-Time Systems Using Network Invariants

Real-time systems often have to cope with an unbounded number of components. For example, an operating system scheduler has to be able to manage an arbitrary number of threads. At the same time, the correctness of central control units such as schedulers is crucial for the correctness of the whole system. However, the comprehensive and semi-automatic verification of real-time systems that are parameterized with an unbounded number of components is still an open problem. In this paper, we propose an approach in which parameterized systems can be verified using a combination of theorem proving and model checking. The interactive theorem prover is used for the overall verification task delegating subsequent proof-goals to automatic verification tools. The central proof method is based on network invariants. The idea of network invariants is to over approximate all instances of a parameterized system and to perform the verification on the abstract model. We have adopted an existing network invariant approach for the verification of centralized real-time systems such as schedulers and formalized the theory in the Isabelle/HOL theorem prover. Preliminary results on applying our framework to small examples are promising and make it worth to evaluate the approach with larger case studies in future work.