Embedded systems often need to react in a timely manner. Life-critical or mission-critical ones require assurance that they comply with these real-time requirements. In particular, schedulability analysis is both essential and difficult to get right. Formal methods can help as they are a powerful tool for ensuring properties with the highest assurance level. We describe a case study for the FPP and EDF policies providing end-to-end assurance by connecting the schedulability analysis tool Prosa and the real-time OS kernel RT-CertiKOS, both using the Coq proof assistant to prove their results. Analyzing precisely the key ideas underlying this connection, we improve it to make it more generic and reduce the associated proof burden. We thus sketch a refined method which allows for providing formal schedulability guarantees to other OSes or low-level components with minimal effort.

Formal verification of real-time systems is attractive because these systems often perform critical operations. Unlike non real-time systems, latency and response time guarantees are of critical importance in this setting, as much as functional correctness. Nevertheless, formal verification of real-time OSes usually stops the scheduling analysis at the policy level: they only prove that the scheduler (or its abstract model) satisfies some scheduling policy. In this paper, we go further and connect together Prosa, a verified schedulability analyzer, and RT-CertiKOS, a verified single-core sequential real-time OS kernel. Thus, we get a more general and extensible schedulability analysis proof for RT-CertiKOS, as well a concrete implementation validating Prosa models. It also showcases that it is realistic to connect two completely independent formal developments in a proof assistant.

This paper introduces CertiCAN, a tool produced using the Coq proof assistant for the formal certification of CAN analysis results. Result certification is a process that is light-weight and flexible compared to tool certification, which makes it a practical choice for industrial purposes. The analysis underlying CertiCAN, which is based on a combined use of two well-known CAN analysis techniques, is computationally efficient. Experiments demonstrate that CertiCAN is faster than the corresponding certified combined analysis. More importantly, it is able to certify the results of RTaW-Pegase, an industrial CAN analysis tool, even for large systems. This result paves the way for a broader acceptance of formal tools for the certification of real-time systems analysis results.

This paper presents the first steps toward a formally proven tool for schedulability analysis of tasks with offsets. We formalize and verify the seminal response time analysis of Tindell by extending the Prosa proof library, which is based on the Coq proof assistant. Thanks to Coq's extraction capabilities, this will allow us to easily obtain a certified analyzer. Additionally, we want to build a Coq certifier that can verify the correctness of results obtained using related (but uncertified), already existing analyzers. Our objective is to investigate the advantages and drawbacks of both approaches, namely the certified analysis and the certifier. The work described in this paper as well as its continuation is intended to enrich the Prosa library.