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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
\(\sqsubseteq \) is reflexive, antisymmetric, transitive, and \(u_0\) is the greatest element of U for \(\sqsubseteq \).
- 2.
- 3.
- 4.
http://cadp.inria.fr/man/caesar.bdd.html (when invoked with “-pnml” option) and http://pnml.lip6.fr/pnml2nupn.
- 5.
http://cadp.inria.fr/man/caesar.bdd.html (see compression/decompression).
- 6.
- 7.
References
Amparore, E., et al.: Presentation of the 9th edition of the Model Checking Contest. In: Beyer, D., Huisman, M., Kordon, F., Steffen, B. (eds.) TACAS 2019. LNCS, vol. 11429, pp. 50–68. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17502-3_4
Bouvier, P., Garavel, H., Ponce-de-León, H.: Automatic decomposition of Petri nets into automata networks – a synthetic account. In: Janicki, R., Sidorova, N., Chatain, T. (eds.) PETRI NETS 2020. LNCS, vol. 12152, pp. 3–23. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51831-8_1
Cheng, A., Esparza, J., Palsberg, J.: Complexity Results for 1-Safe Nets. Theoret. Comput. Sci. 147(1–2), 117–136 (1995)
Desel, J., Esparza, J.: Free Choice Petri Nets, Cambridge Tracts in Theoretical Computer Science, vol. 40. Cambridge University Press, Cambridge (1995)
Garavel, H.: Nested-unit Petri nets. J. Logical Algebraic Methods Program. 104, 60–85 (2019)
Garavel, H.: Proposal for Adding Useful Features to Petri-Net Model Checkers, December 2020. https://arxiv.org/abs/2101.05024
Garavel, H., Serwe, W.: State space reduction for process algebra specifications. Theoret. Comput. Sci. 351(2), 131–145 (2006)
ISO/IEC: High-level Petri Nets - Part 2: Transfer Format. International Standard 15909–2:2011, International Organization for Standardization, Geneva (2011)
Janicki, R.: Nets, sequential components and concurrency relations. Theoret. Comput. Sci. 29, 87–121 (1984)
Kovalyov, A.: Concurrency relations and the safety problem for Petri nets. In: Jensen, K. (ed.) ICATPN 1992. LNCS, vol. 616, pp. 299–309. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55676-1_17
Kovalyov, A.: A polynomial algorithm to compute the concurrency relation of a regular STG. In: Yakovlev, A., Gomes, L., Lavagno, L. (eds.) Hardware Design and Petri Nets, chap. 6, pp. 107–126. Springer, Boston, MA, USA, January 2000. https://doi.org/10.1007/978-1-4757-3143-9_6
Kovalyov, A., Esparza, J.: A polynomial algorithm to compute the concurrency relation of free-choice signal transition graphs. In: Proceedings of the 3rd Workshop on Discrete Event Systems (WODES 1996), Edinburgh, Scotland, UK, pp. 1–6 (1996)
Murata, T.: Petri nets: analysis and applications. Proc. IEEE 77(4), 541–580 (1989)
Schmidt, K.: Stubborn sets for standard properties. In: Donatelli, S., Kleijn, J. (eds.) ICATPN 1999. LNCS, vol. 1639, pp. 46–65. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48745-X_4
Semenov, A., Yakovlev, A.: Combining partial orders and symbolic traversal for efficient verification of asynchronous circuits. In: Ohtsuki, T., Johnson, S. (eds.) Proceedings of the 12th International Conference on Computer Hardware Description Languages and their Applications (CHDL 1995), Makuhari, Chiba, Japan. IEEE (1995)
Wiśniewski, R., Karatkevich, A., Adamski, M., Kur, D.: Application of comparability graphs in decomposition of Petri nets. In: Proceedings of the 7th International Conference on Human System Interactions (HSI 2014), Costa da Caparica, Portugal. IEEE (2014)
Acknowledgements
The experiments of Sect. 5.6 have been performed using the French Grid’5000 testbed.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-76983-3_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-76982-6
Online ISBN: 978-3-030-76983-3
eBook Packages: Computer ScienceComputer Science (R0)