Quantitative Hyperproperties: Specification, Taxonomy, and Runtime Monitoring

Objective

Modern software systems underpin critical infrastructure from aviation to healthcare. Their reliability depends not only on whether requirements are met, but also on how well they are met. Two flight controllers may both ensure safety yet differ in robustness to turbulence; two medical devices may both function yet differ in how much information they leak. Boolean hyperproperties relate multiple executions to specify correctness of implementations, but cannot capture their quantitative differences. As the societal importance of software grows, engineers and regulators need tools to measure and compare implementations. The QHyperSTAR project addresses this gap by developing the first formal framework for quantitative hyperproperties (QHPs), which assign numerical scores to implementations based on relations across executions. QHyperSTAR pursues three objectives: (1) a safety-liveness classification of QHPs that reflects their verification complexity, (2) an expressive specification language supporting automated analysis, and (3) memory-efficient runtime monitoring algorithms validated on resource-constrained cyber-physical systems. The main outcomes are a safety-liveness decomposition of QHPs, a specification language with clear complexity results, and an open-source monitoring prototype. By making requirements such as robustness and privacy measurable and automatically analyzable, QHyperSTAR advances formal methods and enables more reliable digital technologies. Under Prof. Finkbeiner’s supervision at CISPA, I will benefit from a strong synergy with the ERC project HYPER, which lays the foundations of boolean hyperproperties, while QHyperSTAR establishes the complementary quantitative axis. In return, by providing the missing infrastructure for QHPs, I will elevate the impact of the group’s successful monitoring framework RTLola. This environment will let me deepen my expertise, expand collaborations, and develop leadership skills for a research career in Europe.