Proving Properties of Discrete-Valued Functions Using Deductive Proof: Application to the Square Root
https://doi.org/10.18255/1818-1015-2019-4-520-533
Abstract
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.
Supporting agencies: This work was supported by the Groupe PSA, a French multinational manufacturer of automobiles and motorcycles sold under the Peugeot, Citro¨en, DS, Opel and Vauxhall brands.
About the Authors
Vassil Todorov
Groupe PSA
France
France
Safouan Taha
CentraleSupelec
France
PhD
France
PhD
Frederic Boulanger
CentraleSupelec
France
PhD
France
PhD
Armando Hernandez
Groupe PSA
France
France
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Review
For citations:
Todorov V., Taha S., Boulanger F., Hernandez A. Proving Properties of Discrete-Valued Functions Using Deductive Proof: Application to the Square Root. Modeling and Analysis of Information Systems. 2019;26(4):520-533. https://doi.org/10.18255/1818-1015-2019-4-520-533
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