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Model Checking Coverability Graphs of Vector Addition Systems

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Mathematical Foundations of Computer Science 2011 (MFCS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6907))

Abstract

A large number of properties of a vector addition system—for instance coverability, boundedness, or regularity—can be decided using its coverability graph, by looking for some characteristic pattern. We propose to unify the known exponential-space upper bounds on the complexity of such problems on vector addition systems, by seeing them as instances of the model-checking problem for a suitable extension of computation tree logic, which allows to check for the existence of these patterns. This provides new insights into what constitutes a “coverability-like” property.

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References

  1. Atig, M.F., Habermehl, P.: On Yen’s path logic for Petri nets. Int. J. Fund. Comput. Sci. 22(4), 783–799 (2011)

    Article  MATH  Google Scholar 

  2. Axelsson, R., Hague, M., Kreutzer, S., Lange, M., Latte, M.: Extended computation tree logic. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 67–81. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Cardoza, E., Lipton, R.J., Meyer, A.R.: Exponential space complete problems for Petri nets and commutative semigroups. In: STOC 1976, pp. 50–54. ACM Press, New York (1976)

    Chapter  Google Scholar 

  4. Chambart, P., Finkel, A., Schmitz, S.: Forward analysis and model checking for trace bounded WSTS. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 49–68. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Demri, S.: On selective unboundedness of VASS. INFINITY 2010. Elec. Proc. In: Elec. Proc. in Theor. Comput. Sci., vol. 39, pp. 1–15 (2010)

    Google Scholar 

  6. Esparza, J.: Decidability of model checking for infinite-state concurrent systems. Acta Inf. 34(2), 85–107 (1997)

    Article  MathSciNet  Google Scholar 

  7. Figueira, D., Figueira, S., Schmitz, S., Schnoebelen, P.: Ackermannian and primitive-recursive bounds with Dickson’s Lemma. LICS 2011. IEEE, Los Alamitos (2011)

    Google Scholar 

  8. Finkel, A., Sangnier, A.: Reversal-bounded counter machines revisited. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 323–334. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Ganty, P., Majumdar, R., Rybalchenko, A.: Verifying liveness for asynchronous programs. In: POPL 2009, pp. 102–113. ACM Press, New York (2009)

    Google Scholar 

  10. Habermehl, P.: On the complexity of the linear-time μ-calculus for Petri nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 102–116. Springer, Heidelberg (1997)

    Google Scholar 

  11. Hack, M.: Decision problems for Petri nets and vector addition systems. Computation Structures Group Memo 95, Project MAC. MIT, Cambridge (1974)

    Google Scholar 

  12. Hopcroft, J., Pansiot, J.J.: On the reachability problem for 5-dimensional vector addition systems. Theor. Comput. Sci. 8(2), 135–159 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kaiser, A., Kroening, D., Wahl, T.: Dynamic cutoff detection in parameterized concurrent programs. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 645–659. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kosaraju, S.R.: Decidability of reachability in vector addition systems. In: STOC 1982, pp. 267–281. ACM Press, New York (1982)

    Chapter  Google Scholar 

  16. Leroux, J.: Vector addition system reachability problem: a short self-contained proof. In: POPL 2011, pp. 307–316. ACM Press, New York (2011)

    Google Scholar 

  17. Mayr, E.W.: An algorithm for the general Petri net reachability problem. In: STOC 1981, pp. 238–246. ACM Press, New York (1981)

    Chapter  Google Scholar 

  18. Rackoff, C.: The covering and boundedness problems for vector addition systems. Theor. Comput. Sci. 6(2), 223–231 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rosier, L.E., Yen, H.C.: A multiparameter analysis of the boundedness problem for vector addition systems. J. Comput. Syst. Sci. 32(1), 105–135 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  20. Valk, R., Vidal-Naquet, G.: Petri nets and regular languages. J. Comput. Syst. Sci. 23(3), 299–325 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  21. Weispfenning, V.: The complexity of almost linear Diophantine problems. J. Symb. Comput. 10(5), 395–403 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  22. Yen, H.C.: A unified approach for deciding the existence of certain Petri net paths. Inform. and Comput. 96(1), 119–137 (1992)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LSV, ENS Cachan & CNRS, Cachan, France

    Michel Blockelet & Sylvain Schmitz

Authors
  1. Michel Blockelet
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  2. Sylvain Schmitz
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Editor information

Editors and Affiliations

  1. Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Filip Murlak  & Piotr Sankowski  & 

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Blockelet, M., Schmitz, S. (2011). Model Checking Coverability Graphs of Vector Addition Systems. In: Murlak, F., Sankowski, P. (eds) Mathematical Foundations of Computer Science 2011. MFCS 2011. Lecture Notes in Computer Science, vol 6907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22993-0_13

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  • DOI: https://doi.org/10.1007/978-3-642-22993-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22992-3

  • Online ISBN: 978-3-642-22993-0

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