Model Checking Semi � Continuous Time Models Using

The veri cation of timed systems is extremely important but also extremely di cult Several methods have been proposed to assist in this task including extensions to symbolic model checking One possible use of model checking to analyze timed systems is by modeling passage of time as the number of taken transitions and ap plying quantitative algorithms to determine the timing parameters of the system The advantage of this method is its simplicity and e ciency In this paper we extend this technique in two ways First we present new quantitative algorithms that are more e cient than their predecessors The new algorithms determine the number of occurrences of events in all paths between a set of starting states and a set of nal states We then use these algorithms to introduce a new model of time in which the passage of time is dissociated from the occurrence of events With this new model it is possible to verify systems that were previously thought to require dense time models We use the new method to verify two such examples previously analyzed by the HyTech tool a steam boiler example and a fuel injection controller