The Inverse Method

This book introduces state-of-the-art verification techniques for real time embedded systems, based on the inverse method for parametric timed automata. It reviews popular formalisms for the specification and the verification of timed concurrent systems, and in particular timed automata and several extensions such as timed automata equipped with stopwatches, linear hybrid automata and affine hybrid automata. The inverse method is introduced, and its interest for guaranteeing robustness in real time systems is shown. Then it is shown how an iteration of the inverse method can solve the good parameters problem for parametric timed automata, by computing a behavioral cartography of the system. Different extensions are proposed, in particular for hybrid systems, and for applications to scheduling problems using timed automata with stopwatches. Various examples, both from the literature and from the industry, illustrate the techniques throughout the book. In particular, we perform parametric verification of abstractions of a memory circuit sold by the chipset manufacturer ST-Microelectronics, as well as of the prospective flight control system of the next generation of spacecrafts designed by ASTRIUM Space Transportation.