Event Order Abstraction for Parametric Real-Time System Verification
We present a new abstraction technique, event order abstraction (EOA), for parametric safety verification of real-time systems in which ``correct orderings of events'' needed for system correctness are maintained by timing constraints on the systems' behavior. By using EOA, one can separate the task of verifying a real-time system into two parts: 1. Safety property verification of the system given that only correct event orderings occur; and 2. Derivation of timing parameter constraints for correct orderings of events in the system.The user first identifies a candidate set of bad event orders.Then, by using ordinary untimed model-checking, the user examines whether a discretized system model in which all timing constraints are abstracted away satisfies a desirable safety property under the assumption that the identified bad event orders occur in no system execution. The user uses counterexamples obtained from the model-checker to identify additional bad event orders, and repeats the process until the model-checking succeeds. In this step, the user obtains a sufficient set of bad event orders that must be excluded by timing synthesis for system correctness.Next, the algorithm presented in the paper automatically derives a set of timing parameter constraints under which the system does not exhibit the identified bad event orderings. From this step combined with the untimed model-checking step,the user obtains a sufficient set of timing parameter constraints under which the system executes correctly with respect to a given safety property.We illustrate the use of EOA with a train-gate example inspired by the general railroad crossing problem. We also summarize three other case studies, a biphase mark protocol, the IEEE 1394 root contention protocol, and the Fischer mutual exclusion algorithm.