Major - Formal Methods and Foundations of Cyber-Physical Systems (CPS)

Our society relies on complex and autonomous software to control different systems (e.g., autonomous cars and transportation systems, smart grids, drone swarms, medical devices, etc.). Designing and implementing reliable, secure, and high-performance soft-ware for such Cyber-Physical Systems (CPS) is of paramount importance, as software bugs may have serious consequences. However, this task is extremely challenging due to factors such as interaction with the physical environment, communication with other sys-tems, and autonomy.

The CPS major focuses on formal methods — that is, rigorous mathematical techniques — for the specification, analysis, and verification of Cyber-Physical Systems.

The program is research-oriented: it covers the theoretical foundations of CPS and in-cludes two research internships. By the end of the program, students will be able to de-velop new theories and algorithms to analyse CPSs, rather than merely apply existing ones.

Highly qualified applicants are also invited to apply to the Ph.D. track in Computer Sci-ence, specifying CPS as their major and motivating their interest in research and studying in the CPS major.

The first year of the program covers the core principles of formal methods (e.g., abstract interpretation, model checking, ...) as well as computer systems and programs (e.g., compilation). Students have a wide choice of elective courses to gain knowledge of cross-disciplinary topics (e.g., machine learning, distributed systems, ...).

The second year delves deeper into advanced research topics (e.g., formal verification of neural networks and neural network–controlled systems, formal security analysis, etc.) while still allowing students to explore cross-disciplinary subjects.

In each years, the students complete a research internship, primarily within an academic institution (e.g., laboratories of the Institut Polytechnique de Paris).

Objectives

• Acquire the fundamentals of formal methods (e.g., model-checking, abstract interpreta-tion, proof methods and assistants, SAT and SMT, ...)
• Acquire the theoretical notions of Cyber-Physical Systems (e.g., real-time systems, dis-tributed systems, control…)
• Develop new theories and algorithms to analyze CPSs, rather than merely apply existing ones.
• Develop the skills required to pursue a Ph.D. and a career in research (problem solving, abstract thinking, ...)