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We explore in this paper a novel approach that builds an overapproximation ofthe state space of preemptive real time systems. Our graph construction extendsthe expression of a class to the time distance system that encodes thequantitative properties of past fired subsequences. This makes it possible torestore relevant time information that is used to tighten still more the DBMoverapproximation of reachable classes. We succeed thereby to build efficientlytighter approximated graphs which are more appropriate to restore thequantitative properties of the model. The simulation results show that thecomputed graphs are of the same size as the exact graphs while improving by farthe times needed for their computation.

Time distance based computation of the state space of preemptive real time systems