Automated Compositional Proofs for Real-Time Systems

We present a framework for formally proving that the composition of the behaviors of the different parts of a complex, real-time system ensures a desired global specification of the overall system. The framework is based on a simple compositional rely/guarantee circular inference rule, plus a small set of conditions concerning the integration of the different parts into a whole system. The reference specification language is the TRIO metric linear temporal logic. The novelty of our approach with respect to existing compositional frameworks — most of which do not deal explicitly with real-time requirements — consists mainly in its generality and abstraction from any assumptions about the underlying computational model and from any semantic characterizations of the temporal logic language used in the specification. Moreover, the framework deals equally well with continuous and discrete time. It is supported by a tool, implemented on top of the proof-checker PVS, to perform deduction-based verification through theorem-proving of modular real-time axiom systems. As an example of application, we show the verification of a real-time version of the old-fashioned but still relevant “benchmark” of the dining philosophers problem.