Proving Properties of Discrete-Valued Functions Using Deductive Proof: Application to the Square Root

Vassil Todorov (1, 2, 3) , Safouan Taha (1, 4) , Frédéric Boulanger (1, 4) , Armando Hernandez (2)

1 LRI - Laboratoire de Recherche en Informatique
2 Groupe PSA - Centre Technique de Vélizy [Vélizy-Villacoublay]
3 Université Paris-Saclay
4 CentraleSupélec

For many years, automotive embedded systems have been validated only by testing. In the near future, Advanced Driver Assistance Systems (ADAS) will take a greater part in the car's software design and development. Furthermore, their increasing critical level may lead authorities to require a certification for those systems. We think that bringing formal proof in their development can help establishing safety properties and get an efficient certification process. Other industries (e.g. aerospace, railway, nuclear) that produce critical systems requiring certification also took the path of formal verification techniques. One of these techniques is deductive proof. It can give a higher level of confidence in proving critical safety properties and even avoid unit testing. In this paper, we chose a production use case: a function calculating a square root by linear interpolation. We use deductive proof to prove its correctness and show the limitations we encountered with the off-the-shelf tools. We propose approaches to overcome some limitations of these tools and succeed with the proof. These approaches can be applied to similar problems, which are frequent in the automotive embedded software.

Mots clés: formal methods; deductive proof; proving discrete-valued functions

Domaines: Théorie et langage formel [cs.FL]; Génie logiciel [cs.SE]; Modélisation et simulation

Vassil Todorov, Safouan Taha, Frédéric Boulanger, Armando Hernandez. Proving Properties of Discrete-Valued Functions Using Deductive Proof: Application to the Square Root. Modeling and Analysis of Information Systems, 2019, 26 (4), pp.520-533. ⟨10.18255/1818-1015-2019-4-520-533⟩. ⟨hal-02668283⟩