The goal of the project is the design of controllers for swarm robots. Whereas statistical learning from robot logs has encountered several successes to design low-level controllers for a single robot to perform a given task, it is limited first by the quality of the available traces and their adequacy with the target task, and also by possible frequent ambiguities in bothe the environment and the behavioral landscape of the robot. In this context, the originality of this project is twofold: on the one hand, symbolic learning from robot log (either human-driven or controlled by already-learned low-level controllers) will allow the designer to identify landmarks. Such landmarks will then be used to improve the low-level controllers. Secondly, this virtuous circle will be applied not only to single robots, but to swarms of robots, and additional difficulties will rise from the mandatory coordination of the robots, i.e. the necessity to synchronize the different traces before being able to efficiently learn from them collectively. The French team in the project is specialized in statistical learning, with applications in robot control. The Japanese team has a large experience of mining huge amounts of data, and will take care of the symbolic learning part of the project.

The use of computers for formulating conjectures, but also for substantiating proof steps, pervades mathematics, even in its most abstract fields. Most computer proofs are produced by symbolic computations, using computer algebra systems. Sadly, these systems suffer from severe, intrinsic flaws, key to their amazing efficiency, but preventing any flavor of post-hoc verification. But can computer algebra become reliable while remaining fast? Bringing a positive answer to this question represents an outstanding scientific challenge per se, which this project aims at solving. Our starting point is that interactive theorem provers are the best tools for representing mathematics in silico. But we intend to disrupt their architecture, shaped by decades of applications in computer science, so as to dramatically enrich their programming features, while remaining compatible with their logical foundations. We will then design a novel generation of mathematical software, based on the firm grounds of modern programming language theory. This environment will feature a new, high-level, performance-oriented programming language, devised for writing efficient and correct code easily, and for serving the frontline of research in computational mathematics. Users will have access to fast implementations, and to powerful proving technologies for verifying any component à la carte, with high productivity. Logic- and computer-based formal proofs will prevent run-time errors, and incorrect mathematical semantics. We will maintain a close, continuous collaboration with interested high-profile mathematicians, on the verification of cutting-edge research results, today beyond the reach of formal proofs. We ambition to empower mathematical journals to install high-quality artifact evaluation, when peer-reviewing falls short of assessing computer proofs. This project will eventually impact the use of formal methods in engineering, in areas like cryptography or signal-processing.