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Mixing Coverability and Reachability to Analyze VASS with One Zero-Test

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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))

Abstract

We study Vector Addition Systems with States (VASS) extended in such a way that one of the manipulated integer variables can be tested to zero. For this class of system, it has been proved that the reachability problem is decidable. We prove here that boundedness, termination and reversal-boundedness are decidable for VASS with one zero-test. To decide reversal-boundedness, we provide an original method which mixes both the construction of the coverability graph for VASS and the computation of the reachability set of reversal-bounded counter machines. The same construction can be slightly adapted to decide boundedness and hence termination.

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Author information

Authors and Affiliations

  1. LSV, ENS Cachan & CNRS, France

    Alain Finkel

  2. Dipartimento di Informatica, Università di Torino, Italy

    Arnaud Sangnier

Authors
  1. Alain Finkel
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  2. Arnaud Sangnier
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Editor information

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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Finkel, A., Sangnier, A. (2010). Mixing Coverability and Reachability to Analyze VASS with One Zero-Test. 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_33

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  • DOI: https://doi.org/10.1007/978-3-642-11266-9_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11265-2

  • Online ISBN: 978-3-642-11266-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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