Continuous Veri cation by Discrete Reasoning

Two semantics are commonly used for the behavior of real-time and hybrid systems: a discrete semantics, in which the temporal evolution is represented as a sequence of snapshots describing the state of the system at certain times, and a continuous semantics, in which the temporal evolution is represented by a series of time intervals, and therefore corresponds more closely to the physical reality. Powerful veri cation rules are known for temporal logic formulas based on the discrete semantics. This paper shows how to transfer the veri cation techniques of the discrete semantics to the continuous one. We show that if a temporal logic formula has the property of nite variability, its validity in the discrete semantics implies its validity in the continuous one. This leads to a veri cation method based on three components: veri cation rules for the discrete semantics, axioms about time, and some temporal reasoning to bring the results together. This approach enables the veri cation of properties of real-time and hybrid systems with respect to the continuous semantics. This research was supported in part by the National Science Foundation under grant CCR-92-23226, by the Defense Advanced Research Projects Agency under contract NAG2-892, and, by the United States Air Force O ce of Scienti c Research under contract F49620-93-1-0139.