Soundness test cases generation for duration systems

In this paper, we are interested in testing duration systems. Duration systems are an extension of real-time systems for which delays that separate events depend on the accumulated times spent by the computation at some particular locations of the system. We present an automatic testing method for duration systems that uses the approximation method. This method extends a model using an over approximation, the approximate model, containing the digitization timed words of all the real computations of the duration system. Second, we present our conformance relation applied on the approximate model, we demonstrate that test cases generated from the approximate model are soundness test cases. At the end, we propose an algorithm that generate a set of test case presented in a tree by considering a discrete time and how we execute those test cases on the implementation by considering a continuous time.