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A Lazy Query Scheme for Reachability Analysis in Petri Nets

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Book cover Application and Theory of Petri Nets and Concurrency (PETRI NETS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12734))

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Abstract

In recent works we proposed a lazy algorithm for reachability analysis in networks of automata. This algorithm is optimistic and tries to take into account as few automata as possible to perform its task. In this paper we extend the approach to the more general settings of reachability analysis in unbounded Petri nets and reachability analysis in bounded Petri nets with inhibitor arcs. We consider we are given a reachability algorithm and we organize queries to it on bigger and bigger nets in a lazy manner, trying thus to consider as few places and transitions as possible to make a decision. Our approach has been implemented in the Romeo model checker and tested on benchmarks from the model checking contest.

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Notes

  1. 1.

    It uses the classical list data structure. The length of a list L is given by length(L). The \(k^{th}\) element of L is L[k].

  2. 2.

    64bits Linux binaries for Romeo and converters from pnml (MCC) to cts (Romeo), and full results are at http://lara.rts-software.org/.

References

  1. Akshay, S., Chakraborty, S., Das, A., Jagannath, V., Sandeep, S.: On Petri nets with hierarchical special arcs. In: CONCUR, pp. 40:1–40:17 (2017)

    Google Scholar 

  2. Behrmann, G., David, A., Larsen, K.G.: A tutorial on UPPAAL. In: International School on Formal Methods for the Design of Computer, Communication and Software Systems, pp. 200–236 (2004)

    Google Scholar 

  3. Bonet, B., Haslum, P., Hickmott, S., Thiébaux, S.: Directed unfolding of Petri nets. ToPNOC 1(1), 172–198 (2008)

    Google Scholar 

  4. Chatain, T., Paulevé, L.: Goal-driven unfolding of Petri nets. In: CONCUR, pp. 18:1–18:16 (2017)

    Google Scholar 

  5. Couvreur, J.-M., Thierry-Mieg, Y.: Hierarchical decision diagrams to exploit model structure. In: Wang, F., (ed.) FORTE, pp. 443–457 (2005)

    Google Scholar 

  6. Esparza, J., Römer, S., Vogler, W.: An improvement of McMillan’s unfolding algorithm. In: TACAS, pp. 87–106 (1996)

    Google Scholar 

  7. Holzmann, G.J., Peled, D.: An improvement in formal verification. In: FORTE, pp. 197–211 (1994)

    Google Scholar 

  8. Jezequel, L., Lime, D.: Lazy reachability analysis in distributed systems. In: CONCUR, pp. 17:1–17:14 (2016)

    Google Scholar 

  9. Jezequel, L., Lime, D.: Let’s be lazy, we have time - or, lazy reachability analysis for timed automata. In: FORMATS, pp. 247–263 (2017)

    Google Scholar 

  10. Kordon, F., et al.: Complete Results for the 2020 Edition of the Model Checking Contest, June 2020. http://mcc.lip6.fr/2020/results.php

  11. Kordon, F., et al.: MCC’2015 - the fifth model checking contest. ToPNOC 11, 262–273 (2016)

    MathSciNet  Google Scholar 

  12. Rao Kosaraju, S.: Decidability of reachability in vector addition systems (preliminary version). In: Lewis, H.R., Simons, B.B., Burkhard, W.A., Landweber, L.H. (eds.) STOC, pp. 267–281. ACM (1982)

    Google Scholar 

  13. Lambert, J.-L.: A structure to decide reachability in Petri nets. TCS 99(1), 79–104 (1992)

    Article  MathSciNet  Google Scholar 

  14. Lehmann, A., Lohmann, N., Wolf, K.: Stubborn sets for simple linear time properties. In: ICATPN, pp. 228–247 (2012)

    Google Scholar 

  15. Leroux, J., Schmitz, S.: Demystifying reachability in vector addition systems. In: LICS, pp. 56–67. IEEE Computer Society (2015)

    Google Scholar 

  16. Lime, D., Roux, O.H., Seidner, C., Traonouez, L.-M.: Romeo: a parametric model-checker for Petri nets with stopwatches. In: TACAS, pp. 54–57 (2009)

    Google Scholar 

  17. Mayr, E.W.: An algorithm for the general Petri net reachability problem. SIAM J. Comput. 13(3), 441–460 (1984)

    Article  MathSciNet  Google Scholar 

  18. McMillan, K.: Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In: CAV, pp. 164–177 (1993)

    Google Scholar 

  19. Miner, A., Babar, J.: Meddly: multi-terminal and edge-valued decision diagram library. In: QEST, pp. 195–196 (2010)

    Google Scholar 

  20. Reinhardt, K.: Reachability in Petri nets with inhibitor arcs. ENTCS 223, 239–264 (2008)

    MATH  Google Scholar 

  21. Weiser, M.: Program slicing. IEEE Trans. Softw. Eng. SE-10(4), 352–357 (1984)

    Google Scholar 

  22. Wolf, K.: Running LoLA 2.0 in a model checking competition. ToPNOC 11, 274–285 (2016)

    Google Scholar 

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Correspondence to Loïg Jezequel .

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Jezequel, L., Lime, D., Sérée, B. (2021). A Lazy Query Scheme for Reachability Analysis in Petri Nets. In: Buchs, D., Carmona, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2021. Lecture Notes in Computer Science(), vol 12734. Springer, Cham. https://doi.org/10.1007/978-3-030-76983-3_18

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  • DOI: https://doi.org/10.1007/978-3-030-76983-3_18

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  • Print ISBN: 978-3-030-76982-6

  • Online ISBN: 978-3-030-76983-3

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