System Verification and Runtime Monitoring with Multiple Weakly-Hard Constraints

A weakly-hard fault model can be captured by an (m,k) constraint, where 0≤ m≤ k, meaning that there are at most m bad events (faults) among any k consecutive events. In this article, we use a weakly-hard fault model to constrain the occurrences of faults in system inputs. We develop approaches to verify properties for all possible values of (m,k), where k is smaller than or equal to a given K, in an exact and efficient manner. By verifying all possible values of (m,k), we define weakly-hard requirements for the system environment and design a runtime monitor based on counting the number of faults in system inputs. If the system environment satisfies the weakly-hard requirements, then the satisfaction of desired properties is guaranteed; otherwise, the runtime monitor can notify the system to switch to a safe mode. This is especially essential for cyber-physical systems that need to provide guarantees with limited resources and the existence of faults. Experimental results with discrete second-order control, network routing, vehicle following, and lane changing demonstrate the generality and the efficiency of the proposed approaches.