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The Inverse Method

Parametric Verification of Real-time Embedded Systems

Étienne André, University of Paris 13, France Romain Soulat, ENS-Cachan, France

ISBN: 9781848214477

Publication Date: January 2013   Hardback   176 pp.

90.00 USD

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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 verification of timed concurrent systems and, in particular, timed automata as well as several extensions such as timed automata equipped with stopwatches, linear hybrid automata and affine hybrid automata. The inverse method is introduced, and its benefits for guaranteeing robustness in real-time systems are 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 particularly for hybrid systems and applications to scheduling problems using timed automata with stopwatches. Various examples, both from the literature and industry, illustrate the techniques throughout the book. Various parametric verifications are performed, in particular 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 spacecraft designed by ASTRIUM Space Transportation.


1. Parametric Timed Automata.
2. The Inverse Method for Parametric Timed Automata.
3. The Inverse Method in Practice: Application to Case Studies.
4. Behavioral Cartography of Timed Automata.
5. Parameter Synthesis for Hybrid Automata.
6. Application to the Robustness Analysis of Scheduling Problems.
7. Conclusion and Perspectives.

About the Authors

Étienne André is Associate Professor in the Laboratoire d’Informatique de Paris Nord, in the University of Paris 13 (Sorbonne Paris Cité) in France. His current research interests focus on the verification of real-time systems.
Romain Soulat is currently completing his PhD at the LSV laboratory at ENS-Cachan in France, focusing on the modeling and verification of hybrid temporal systems.


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