Inductive Verification of Hybrid Automata with Strongest Postcondition Calculus

Daisuke Ishii (1) , Guillaume Melquiond (2, 3) , Shin Nakajima (1)

1 NII - National Institute of Informatics
2 LRI - Laboratoire de Recherche en Informatique
3 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations

Safety verification of hybrid systems is a key technique in developing embedded systems that have a strong coupling with the physical environment. We propose an automated logical analytic method for verifying a class of hybrid automata. The problems are more general than those solved by the existing model checkers: our method can verify models with symbolic parameters and nonlinear equations as well. First, we encode the execution trace of a hybrid automaton as an imperative program. Its safety property is then translated into proof obligations by strongest postcondition calculus. Finally, these logic formulas are discharged by state-of-the-art arithmetic solvers (e.g., Mathematica). Our proposed algorithm efficiently performs inductive reasoning by unrolling the execution for some steps and generating loop invariants from verification failures. Our experimental results along with examples taken from the literature show that the proposed approach is feasible.

Mots clés: hybrid systems; safety analysis; Hoare logic; strongest postconditions; invariant generation

Domaines: Génie logiciel [cs.SE]; Systèmes dynamiques [math.DS]

Daisuke Ishii, Guillaume Melquiond, Shin Nakajima. Inductive Verification of Hybrid Automata with Strongest Postcondition Calculus. iFM - 10th International Conference on Integrated Formal Methods - 2013, Jun 2013, Turku, Finland. pp.139-153, ⟨10.1007/978-3-642-38613-8_10⟩. ⟨hal-00806701⟩