Section: Research Program

Model expressivity and quantitative verification

The overall objective of this axis is to combine the quantitative aspects of models with a distributed/modular setting, while maintaining the tractability of verification and management objectives.

There is first an issue of modeling, to nicely weave time, costs and probabilities with concurrency and/or asynchronism. Several approaches are quite natural, as time(d) Petri nets, networks of timed automata, communicating synchronously or through FIFO, etc. But numerous bottlenecks remain. For example, so far, no probabilistic model nicely fits the notion of concurrency: there is no clean way to express that two components are stochastically independent between two rendez-vous.

Second, the models we want to manipulate should allow for quantitative verification. This covers two aspects: either the verification question is itself quantitative (compute an optimal scheduling policy) or boolean (decide whether the probability is greater than a threshold). Our goal is to explore the frontier between decidable and undecidable problems, or more pragmatically tractable and untractable problems. Of course, there is a tradeoff between the expressivity and the tractability of a model. Models that incorporate distributed aspects, probabilities, time, etc, are typically untractable. In such a case, abstraction or approximation techniques are a work around that we will explore.

In more details, our research program on this axis covers questions like:

• the verification of distributed timed systems,

• the verification of large scale probabilistic (dynamic) systems, with a focus on approximation techniques for such systems,

• the evaluation of the opacity/diagnosability degree of stochastic systems,

• the design of modular testing methods for large scale modular systems.