Section: Research Program

Axis 1: Quantitative models

The analysis and control of quantitative models will remain at the heart of a large part of our research activities. In particular, we have two starting collaborative projects focusing on timed models, namely our ANR project TickTac and our collaboration with MERCE. The main expected outcome of TickTac is an open-source tool implementing the latest algorithms and allowing for quick prototyping of new algorithms. Several other topics will be explored in these collaborations, including robustness issues, game-theoretic problems, as well as the development of efficient algorithms, e.g. based on CEGAR approach or specifically designed for subclasses of automata (e.g. automata with few clocks and/or having a specific structure, as in  [38]). Inspired by our collaboration with Alstom, we also aim at developing symbolic techniques for analysing non-linear timed models.

Stochastic models are another important focus for our research. On the one hand, we want to pursue our work on the optimization of non-standard properties for Markov decision processes, beyond the traditional verification questions, and explore e.g. long-run probabilities, and quantiles. Also, we aim at lifting our work on decisiveness from purely stochastic  [36], [37] to non-deterministic and stochastic models in order to provide approximation schemes for the probability of (repeated) reachability properties in infinite-state Markov decision processes. On the other hand, in order to effectively handle large stochastic systems, we will pursue our work on approximation techniques. We aim at deriving simpler models, enjoying or preserving specific properties, and at determining the appropriate level of abstraction for a given system. One needs of course to quantify the approximation degrees (distances), and to preserve essential features of the original systems (explainability). This is a connection point between formal methods and the booming learning methods.

Regarding diagnosis/opacity issues, we will explore further the quantitative aspects. For diagnosis, the theory needs extensions to the case of incomplete or erroneous models, and to reconfigurable systems, in order to develop its applicability (see Sec. 3.6). There is also a need for non-binary causality analysis (e.g. performance degradations in complex systems). For opacity, we aim at quantifying the effort attackers must produce vs how much of a secret they can guess. We also plan to synthesize robust controllers resisting to sensor failures/attacks.