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Forcing Monotonicity in Parameterized Verification: From Multisets to Words

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SOFSEM 2010: Theory and Practice of Computer Science (SOFSEM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5901))

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Abstract

We present a tutorial on verification of safety properties for parameterized systems. Such a system consists of an arbitrary number of processes; the aim is to prove correctness of the system regardless of the number of processes inside the system. First, we consider a class of parameterized systems whose behaviours can be captured exactly as Petri nets using counter abstraction. This allows analysis using the framework of monotonic transition systems introduced in [1]. Then, we consider parameterized systems for which there is no natural ordering which allows monotonicity. We describe the method of monotonic abstraction which provides an over-approximation of the transition system. We consider both systems where the over-approximation gives rise to reset Petri nets, and systems where the abstract transition relation is a set of rewriting rules on words over a finite alphabet.

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Authors and Affiliations

  1. Department of Information Technology, Uppsala University, P.O. Box 337, 751 05, Uppsala, Sweden

    Parosh Aziz Abdulla

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  1. Parosh Aziz Abdulla
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Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH, Utrecht, The Netherlands

    Jan van Leeuwen

  2. LaBRI, Universit Bordeaux, 351 cours de la Libration, 1F-33405, Talence Cedex, France

    Anca Muscholl

  3. Department of Computer Science & Applied Mathematics, Weizmann Institute, Faculty of Mathematics and Computer Science, 76100, Rehovot, Israel

    David Peleg

  4. Department of Software Engineering Faculty of Mathematics and Physics Malostranské nám, Charles University, 25 11800, Prague 1, Czech Republic

    Jaroslav Pokorný

  5. Software Engineering, Department of Computer Science, RWTH Aachen University, 3, Ahornstrae 55, D-52074, Aachen, Germany

    Bernhard Rumpe

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Abdulla, P.A. (2010). Forcing Monotonicity in Parameterized Verification: From Multisets to Words. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-11266-9_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11265-2

  • Online ISBN: 978-3-642-11266-9

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