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

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.

A Method for Measuring the Constraint Complexity of Components in Automotive Embedded Software Systems

The rapid growth of software-based functionalities has made automotive Electronic Control Units (ECUs) significantly complex. Factors affecting the software complexity of components embedded in an ECU depend not only on their interface and interaction properties, but also on the structural constraints characterized by a component’s functional semantics and timing constraints described by AUTomotive Open System ARchitecture (AUTOSAR) languages. Traditional constraint complexity measures are not adequate for the components in embedded software systems as they do not yet sufficiently provide a measure of the complexity due to timing constraints which are important for quantifying the dynamic behavior of components at run-time. This paper presents a method for measuring the constraint complexity of components in automotive embedded software systems at the specification level. It first enables system designers to define non-deterministic constraints on the event chains associated with components using the AUTOSAR-based Modeling and Analysis of Real-Time and Embedded systems (MARTE)-UML and Timing Augmented Description Language (TADL). Then, system analysts use Unified Modeling Language (UML)-compliant Object Constraint Language (OCL) and its Real-time extension (RT-OCL) to specify the structural and timing constraints on events and event chains and estimate the constraint complexity of components using a measure we have developed. A preliminary version of the method was presented in M. Garg and R. Lai, Measuring the constraint complexity of automotive embedded software systems, in Proc. Int. Conf. Data and Software Engineering, 2014, pp. 1–6. To demonstrate the usefulness of our method, we have applied it to an automotive Anti-lock Brake System (ABS).