Proving Partial-Correctness and Invariance Properties of Transition-System Models

Vlad Rusu, Grimaud, Gilles, Hauspie, Micha{\"e}l. Proving Partial-Correctness and Invariance Properties of Transition-System Models. In TASE 2018 - 12th International Symposium on Theoretical Aspects of Software Engineering. IEEE Xplore, Guangzhou, China, Aug 2018.

Abstract

We propose a deductive verification approach for proving partial-correctness and invariance properties on transition-system models. Regarding partial correctness, we gen-eralise the recently introduced formalism of Reachability Logic, currently used as a language-parametric logic for programs, to transition systems. We propose a sound and relatively complete proof system for the resulting reachability logic. The soundness of the proof system is formally established in the Coq proof assistant, and the mechanised proof provides us with a Coq-certified Reachability-Logic prover for transition-system models. The relative completeness of the proof system, although theoretical in nature, also has a practical value, as it induces a proof strategy that is guaranteed to prove all valid formulas on a given transition system. The strategy reduces partial-correctness verification to invariance verification; for the latter we propose an incremental technique in order to deal with the case-explosion problem that affects it. All these techniques were instrumental in enabling us to prove, within reasonable time and effort limits, that the nontrivial algorithm implemented in security hypervisor that we designed in earlier work meets its expected functional requirements.

PDF available at https://hal.inria.fr/view/index/docid/1895650.