Safety Verification Based on Fluidification of Discrete Dynamics

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For generalized stochastic Petri nets with exponentially distributed firing delay, we propose a method for approximating variance of the probability distribution in each place by introducing interval firing speeds on the fluid model. We next show that the models are equivalently represented by piecewise linear systems with interval parameters. For simulation of the models, two methods are proposed : one is an extension of the interval methods for ordinary differential equations, and the other is acceleration technique for the computation in the box abstraction, a discrete abstraction technique for continuous-state systems.