Efficient System Verification with Multiple Weakly-Hard Constraints for Runtime Monitoring

A weakly-hard fault model can be captured by an (m, k) constraint, where \(0\le m\le k\), meaning that there are at most m bad events (faults) among any k consecutive events. In this paper, 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, the satisfaction of desired properties is guaranteed; otherwise, the runtime monitor can notify the system to switch to a safe mode. Experimental results with a discrete second-order controller demonstrate the efficiency of the proposed approaches.