Abstract
The verification of hybrid systems is intrinsically hard, due to the continuous dynamics that leads to infinite search spaces. Therefore, research attempts focused on hybrid system falsification of a black-box model, a technique that aims at finding an input signal violating the desired temporal specification. Main falsification approaches are based on stochastic hill-climbing optimization, that tries to minimize the degree of satisfaction of the temporal specification, given by its robust semantics. However, in the presence of constraints between the inputs, these methods become less effective. In this article, we solve this problem using a search space transformation that first maps points of the unconstrained search space to points of the constrained one, and then defines the fitness of the former ones based on the robustness values of the latter ones. Based on this search space transformation, we propose a falsification approach that performs the search over the unconstrained space, guided by the robustness of the mapped points in the constrained space. We introduce three versions of the proposed approach that differ in the way of selecting the mapped points. Experiments show that the proposed approach outperforms state-of-the-art constrained falsification approaches.
Highlights
H YBRID Systems FalsificationCyber-physical systems (CPSs) are hybrid systems combining physical and digital components
Quality assurance of CPS is a problem of great importance, automated formal verification of hybrid systems is almost impossible due to their physical components that lead to infinite search spaces
The proportional transformation is surjective, it changes the distribution of fitness on the base of the selected priority, and so it influences the performance of hill-climbing optimization
Summary
Cyber-physical systems (CPSs) are hybrid systems combining physical and digital components. Penalty values that are added to the objective function can modify the fitness landscape (i.e., values of the objective function) in a way (e.g., a large flat plateau with a constant value) that the performance of the search algorithm (e.g., hill climbing) may be affected Another category of constraint handling methods is called feasibility preservation, which consists of repairing the infeasible inputs by moving them to the feasible space. The approach defines a search space transformation mapping each point −→u of an unconstrained search space to a point −→π of the constrained input space, and defines the fitness of −→u in terms of the robustness value of −→π In this way, the approach performs the falsification search over the unconstrained search space, without compromising the effectiveness of hill climbing (differently from what happens with the penalty-based approaches).
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