Parametric Falsification of Many Probabilistic Requirements Under Flakiness

Falsification is a popular simulation-based testing method for Cyber-Physical Systems to find inputs that violate a formal requirement. It employs optimization algorithms to minimize a robustness metric that defines the satisfaction of a given property over an execution trace. Despite falsification representing an established approach, detecting violations considering many, possibly independent, requirements simultaneously, under flaky simulations is an open problem. We address this problem by proposing a novel approach that combines parametric model checking and many-objective optimization. We use parametric model checking to shift part of the complexity of the problem offline. We pre-compute numeric constraints for the satisfaction of all requirements on a parametric specification of the testing scenario. Flaky violations are then detected using many-objective optimization to explore the space of changing factors in the scenario and push the parameters out of all precomputed constraints. The results of our empirical evaluation using four open-source evaluation subjects with increasing complexity (number of requirements) show that our approach can falsify many requirements simultaneously, without hiding their individual contribution. The effectiveness, in terms of quantity and severity of violations, is significantly higher than random search as well as two selected state-of-the-art baseline approaches. Furthermore, the extra offline computation yields a negligible cost.