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Efficient Algorithms for Three Reachability Problems in Safe Petri Nets

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

Abstract

We investigate three particular instances of the marking coverability problem in ordinary, safe Petri nets: the Dead Places Problem, the Dead Transitions Problem, and the Concurrent Places Problem. To address these three problems, which are of practical interest, although not yet supported by mainstream Petri net tools, we propose a combination of static and dynamic algorithms. We implemented these algorithms and applied them to a large collection of 13,000+ Petri nets obtained from realistic systems—including all the safe benchmarks of the Model Checking Contest. Experimental results show that 95% of the problems can be solved in a few minutes using the proposed approaches.

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Notes

  1. 1.

    \(\sqsubseteq \) is reflexive, antisymmetric, transitive, and \(u_0\) is the greatest element of U for \(\sqsubseteq \).

  2. 2.

    http://cadp.inria.fr/man/caesar.bdd.html.

  3. 3.

    http://cadp.inria.fr/man/nupn.html.

  4. 4.

    http://cadp.inria.fr/man/caesar.bdd.html (when invoked with “-pnml” option) and http://pnml.lip6.fr/pnml2nupn.

  5. 5.

    http://cadp.inria.fr/man/caesar.bdd.html (see compression/decompression).

  6. 6.

    http://mcc.lip6.fr/models.php.

  7. 7.

    https://github.com/nicolasAmat/Kong.

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Acknowledgements

The experiments of Sect. 5.6 have been performed using the French Grid’5000 testbed.

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Correspondence to Pierre Bouvier or Hubert Garavel .

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Bouvier, P., Garavel, H. (2021). Efficient Algorithms for Three Reachability Problems in Safe 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_17

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  • DOI: https://doi.org/10.1007/978-3-030-76983-3_17

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