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Recent and simple algorithms for Petri nets

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Abstract

We show how inductive invariants can be used to solve coverability, boundedness and reachability problems for Petri nets. This approach provides algorithms that are conceptually simpler than previously published ones.

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Notes

  1. Words that can be iterated are denoted with the letter \(\sigma \).

References

  1. Bouziane, Z.: A primitive recursive algorithm for the general petri net reachability problem. In: FOCS 1998, pp. 130–136 (1998)

  2. Bozzelli, L., Ganty, P.: Complexity analysis of the backward coverability algorithm for vass. In: Delzanno, G., Potapov, I. (eds.) Reachability Problems—5th International Workshop, RP 2011, Genoa, Italy, September 28–30, 2011. Proceedings. Volume 6945 of Lecture Notes in Computer Science, pp. 96–109. Springer (2011)

  3. Cardoza, E., Lipton, R.J., Meyer, A.R.: Exponential space complete problems for Petri nets and commutative semigroups: preliminary report. In: STOC’76, pp. 50–54. ACM (1976)

  4. Demri, S.: On selective unboundedness of vass. In: Chen, Y.F., Rezine, A. (eds.) Proceedings 12th International Workshop on Verification of Infinite-State Systems. Volume 39 of EPTCS, pp. 1–15 (2010)

  5. Figueira, D., Figueira, S., Schmitz, S., Schnoebelen, P.: Ackermannian and primitive-recursive bounds with Dickson’s lemma. In: Logic in Computer Science (LICS), 2011 26th Annual IEEE Symposium on, pp. 269–278 (2011)

  6. Finkel, A., Schnoebelen, Ph: Well-structured transition systems everywhere!. Theoret. Comput. Sci. 256(1–2), 63–92 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Finkel, A.: The minimal coverability graph for petri nets. In: Rozenberg, G. (ed.) Advances in Petri Nets 1993. Volume 674 of Lect. Notes Comp. Sci. pp. 210–243. Springer (1993)

  8. Finkel, A., Goubault-Larrecq, J.: Forward analysis for WSTS, part I: completions. In: Albers, S., Marion, J.Y. (eds.) 26th Symposium on Theoretical Aspects of Computer Science, STACS’09, pp. 433–444. Springer (2009)

  9. Finkel, A., Goubault-Larrecq, J.: Forward analysis for WSTS, part II: complete WSTS. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S.E., Thomas, W. (eds.) 36th International Colloquium on Automata, Languages and Programming, ICALP’09. Volume 5556 of Lecture Notes Computer Science, pp. 188–199. Springer (2009)

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Jančar, P.: Bouziane’s transformation of the petri net reachability problem and incorrectness of the related algorithm. Inf. Comput. 206, 1259–1263 (2008)

    Article  MATH  Google Scholar 

  12. Leroux, J.: Vector addition systems reachability problem (a simpler solution). In: Voronkov, A. (ed.) The Alan Turing Centenary Conference, Turing-100, Manchester UK June 22–25, 2012, Proceedings. Volume 10 of EPiC Series, EasyChair, pp. 214–228 (2012)

  13. Mayr, E.W., Meyer, A.R.: The complexity of the finite containment problem for petri nets. J. ACM 28(3), 561–576 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  14. Pachl, J.K.: Reachability problems for communicating finite state machines. CoRR cs.LO/0306121 (2003)

  15. Rackoff, Ch.: The covering and boundedness problems for vector addition systems. Theoret. Comput. Sci. 6(2), 223–231 (1978)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

We thank Pierre McKenzie and Wolfgang Reisig for their careful reading of the paper.

Author information

Authors and Affiliations

  1. LSV, ENS Cachan, CNRS, INRIA, Paris, France

    Alain Finkel

  2. LaBRI, CNRS, Université de Bordeaux, Bordeaux, France

    Jérôme Leroux

Authors
  1. Alain Finkel
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  2. Jérôme Leroux
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Corresponding author

Correspondence to Alain Finkel.

Additional information

Communicated by Dr. Wolfgang Reisig.

This work is supported by the french Agence Nationale de la Recherche, REACHARD (Grant ANR-11-BS02-001) and by the “Chaire DIGITEO-ENS CACHAN—ECOLE POLYTECHNIQUE”.

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Finkel, A., Leroux, J. Recent and simple algorithms for Petri nets. Softw Syst Model 14, 719–725 (2015). https://doi.org/10.1007/s10270-014-0426-0

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  • DOI: https://doi.org/10.1007/s10270-014-0426-0

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