Section: New Results

Modular verification of cyber-physical systems using contract theory

Participants : Jean-Pierre Talpin, Benoit Boyer, David Mentre, Simon Lunel.

The primary goal of our project, in collaboration with Mitsubishi Electronics Research Centre Europe (MERCE), is to ensure correctness-by-design in realistic cyber-physical systems, i.e., systems that mix software and hardware in a physical environment, e.g., Mitsubishi factory automation lines or water-plant factory. To achieve that, we develop a verification methodology based on contract reasoning.

We have first performed a state of the art of the research and the work of A. Platzer with the Differential Dynamic Logic ($dℒ$) retained our attention (Differential Dynamic Logic for Hybrid Systems, André Platzer, http://symbolaris.com/logic/dL.html). This a formalism built on the Dynamic Logic of V. Pratt augmented with the possibility of expressing Ordinary Differential Equations (ODEs). ODEs are the usual way to model physical behaviors in physics and $dℒ$ permits to accurately model cyber-physical systems. But this logic can also express properties on real arithmetic and there is proof system associated, under the form of a sequent calculus, which let us a mean to prove specifications. To finish, it is very natural to use contract to specify systems since it was the primary goal of the work of V. Pratt. To conclude, $dℒ$ is particularly fit to our purpose.

We have some preliminary results about a design-by-composition methodology: we have defined a syntactic composition operator in $dℒ$, which enjoys associativity and commutativity. We have then characterized the conditions under which we can derive automatically a proof of the contract of our composition. To exemplified our ideas, we are currently studying a simplified water-tank system, which will serve as a basis for more realistic case studies. We plan to provide refinement and abstraction mechanisms to ultimately allow a mix between vertical and horizontal design.