Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems

We introduce the framework of hybrid automata as a model and speci cation language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of di erential equations. We show that many of the examples considered in the workshop can be de ned by hybrid automata. While the reachability problem is undecidable even for very restricted classes of hybrid automata, we present two semidecision procedures for verifying safety properties of piecewise-linear hybrid automata, in which all variables change at constant rates. The two procedures are based, respectively, on minimizing and computing xpoints on generally in nite state spaces. We show that if the procedures terminate, then they give correct answers. We then demonstrate that for many of the typical workshop examples, the procedures do terminate and thus provide an automatic way for verifying their properties.