Acyclic Petri and Workflow Nets with Resets

Authors Dmitry Chistikov , Wojciech Czerwiński , Piotr Hofman , Filip Mazowiecki, Henry Sinclair-Banks



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Author Details

Dmitry Chistikov
  • Centre for Discrete Mathematics and its Applications (DIMAP) & Department of Computer Science, University of Warwick, Coventry, UK
Wojciech Czerwiński
  • University of Warsaw, Poland
Piotr Hofman
  • University of Warsaw, Poland
Filip Mazowiecki
  • University of Warsaw, Poland
Henry Sinclair-Banks
  • Centre for Discrete Mathematics and its Applications (DIMAP) & Department of Computer Science, University of Warwick, Coventry, UK

Acknowledgements

We would like to thank Alain Finkel for pointing out an error in the introduction. We would also like to thank our anonymous reviewers for their detailed comments.

Cite AsGet BibTex

Dmitry Chistikov, Wojciech Czerwiński, Piotr Hofman, Filip Mazowiecki, and Henry Sinclair-Banks. Acyclic Petri and Workflow Nets with Resets. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.FSTTCS.2023.16

Abstract

In this paper we propose two new subclasses of Petri nets with resets, for which the reachability and coverability problems become tractable. Namely, we add an acyclicity condition that only applies to the consumptions and productions, not the resets. The first class is acyclic Petri nets with resets, and we show that coverability is PSPACE-complete for them. This contrasts the known Ackermann-hardness for coverability in (not necessarily acyclic) Petri nets with resets. We prove that the reachability problem remains undecidable for acyclic Petri nets with resets. The second class concerns workflow nets, a practically motivated and natural subclass of Petri nets. Here, we show that both coverability and reachability in acyclic workflow nets with resets are PSPACE-complete. Without the acyclicity condition, reachability and coverability in workflow nets with resets are known to be equally hard as for Petri nets with resets, that being Ackermann-hard and undecidable, respectively.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • Petri nets
  • Workflow Nets
  • Resets
  • Acyclic
  • Reachability
  • Coverability

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References

  1. Toshiro Araki and Tadao Kasami. Some decision problems related to the reachability problem for Petri nets. Theor. Comput. Sci., 3(1):85-104, 1976. URL: https://doi.org/10.1016/0304-3975(76)90067-0.
  2. Michael Blondin, Christoph Haase, Filip Mazowiecki, and Mikhail A. Raskin. Affine extensions of integer vector addition systems with states. Log. Methods Comput. Sci., 17(3), 2021. URL: https://doi.org/10.46298/lmcs-17(3:1)2021.
  3. Michael Blondin, Filip Mazowiecki, and Philip Offtermatt. The complexity of soundness in workflow nets. In Christel Baier and Dana Fisman, editors, LICS '22: 37th Annual ACM/IEEE Symposium on Logic in Computer Science, Haifa, Israel, August 2-5, 2022, pages 20:1-20:13. ACM, 2022. URL: https://doi.org/10.1145/3531130.3533341.
  4. Michael Blondin, Filip Mazowiecki, and Philip Offtermatt. Verifying generalised and structural soundness of workflow nets via relaxations. In Sharon Shoham and Yakir Vizel, editors, Computer Aided Verification - 34th International Conference, CAV 2022, Haifa, Israel, August 7-10, 2022, Proceedings, Part II, volume 13372 of Lecture Notes in Computer Science, pages 468-489. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-13188-2_23.
  5. Michael Blondin and Mikhail A. Raskin. The complexity of reachability in affine vector addition systems with states. Log. Methods Comput. Sci., 17(3), 2021. URL: https://doi.org/10.46298/lmcs-17(3:3)2021.
  6. Dmitry Chistikov, Christoph Haase, and Simon Halfon. Context-free commutative grammars with integer counters and resets. Theor. Comput. Sci., 735:147-161, 2018. Special issue for RP 2014. URL: https://doi.org/10.1016/j.tcs.2016.06.017.
  7. Wojciech Czerwinski, Slawomir Lasota, Ranko Lazic, Jérôme Leroux, and Filip Mazowiecki. The reachability problem for Petri nets is not elementary. J. ACM, 68(1):7:1-7:28, 2021. URL: https://doi.org/10.1145/3422822.
  8. Wojciech Czerwinski and Lukasz Orlikowski. Reachability in vector addition systems is Ackermann-complete. In 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021, Denver, CO, USA, February 7-10, 2022, pages 1229-1240. IEEE, 2021. URL: https://doi.org/10.1109/FOCS52979.2021.00120.
  9. Catherine Dufourd, Alain Finkel, and Philippe Schnoebelen. Reset nets between decidability and undecidability. In Kim Guldstrand Larsen, Sven Skyum, and Glynn Winskel, editors, Automata, Languages and Programming, 25th International Colloquium, ICALP'98, Aalborg, Denmark, July 13-17, 1998, Proceedings, volume 1443 of Lecture Notes in Computer Science, pages 103-115. Springer, 1998. URL: https://doi.org/10.1007/BFb0055044.
  10. Dirk Fahland, Cédric Favre, Barbara Jobstmann, Jana Koehler, Niels Lohmann, Hagen Völzer, and Karsten Wolf. Instantaneous soundness checking of industrial business process models. In Umeshwar Dayal, Johann Eder, Jana Koehler, and Hajo A. Reijers, editors, Business Process Management, 7th International Conference, BPM 2009, Ulm, Germany, September 8-10, 2009. Proceedings, volume 5701 of Lecture Notes in Computer Science, pages 278-293. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-03848-8_19.
  11. Diego Figueira, Santiago Figueira, Sylvain Schmitz, and Philippe Schnoebelen. Ackermannian and primitive-recursive bounds with Dickson’s lemma. In Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science, LICS 2011, June 21-24, 2011, Toronto, Ontario, Canada, pages 269-278. IEEE Computer Society, 2011. URL: https://doi.org/10.1109/LICS.2011.39.
  12. Alain Finkel, Pierre McKenzie, and Claudine Picaronny. A well-structured framework for analysing Petri net extensions. Inf. Comput., 195(1-2):1-29, 2004. URL: https://doi.org/10.1016/j.ic.2004.01.005.
  13. Christoph Haase, Stephan Kreutzer, Joël Ouaknine, and James Worrell. Reachability in succinct and parametric one-counter automata. In Mario Bravetti and Gianluigi Zavattaro, editors, CONCUR 2009 - Concurrency Theory, 20th International Conference, CONCUR 2009, Bologna, Italy, September 1-4, 2009. Proceedings, volume 5710 of Lecture Notes in Computer Science, pages 369-383. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-04081-8_25.
  14. Kunihiko Hiraishi and Atsunobu Ichikawa. A class of Petri nets that a necessary and sufficient condition for reachability is obtainable. Transactions of the Society of Instrument and Control Engineers, 24(6):635-640, 1988. URL: https://doi.org/10.9746/sicetr1965.24.635.
  15. Alexander Kaiser, Daniel Kroening, and Thomas Wahl. A widening approach to multithreaded program verification. ACM Trans. Program. Lang. Syst., 36(4):14:1-14:29, 2014. URL: https://doi.org/10.1145/2629608.
  16. Marvin Künnemann, Filip Mazowiecki, Lia Schütze, Henry Sinclair-Banks, and Karol Węgrzycki. Coverability in VASS Revisited: Improving Rackoff’s Bound to Obtain Conditional Optimality. In Kousha Etessami, Uriel Feige, and Gabriele Puppis, editors, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023), volume 261 of Leibniz International Proceedings in Informatics (LIPIcs), pages 131:1-131:20, Dagstuhl, Germany, 2023. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ICALP.2023.131.
  17. Jérôme Leroux. The reachability problem for Petri nets is not primitive recursive. In 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021, Denver, CO, USA, February 7-10, 2022, pages 1241-1252. IEEE, 2021. URL: https://doi.org/10.1109/FOCS52979.2021.00121.
  18. Jérôme Leroux and Sylvain Schmitz. Reachability in vector addition systems is primitive-recursive in fixed dimension. In 34th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2019, Vancouver, BC, Canada, June 24-27, 2019, pages 1-13. IEEE, 2019. URL: https://doi.org/10.1109/LICS.2019.8785796.
  19. Duan Li, Xiaoling Sun, Jianjun Gao, Shenshen Gu, and Xiaojin Zheng. Reachability determination in acyclic Petri nets by cell enumeration approach. Autom., 47(9):2094-2098, 2011. URL: https://doi.org/10.1016/j.automatica.2011.06.017.
  20. R. J. Lipton. The reachability problem requires exponential space. Research Report. Department of Computer Science, Yale University, 1976. URL: http://www.cs.yale.edu/publications/techreports/tr63.pdf.
  21. Marvin L. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, Inc., 1967. Google Scholar
  22. C. A. Petri. Introduction to general net theory. In Wilfried Brauer, editor, Net Theory and Applications, Proceedings of the Advanced Course on General Net Theory of Processes and Systems, Hamburg, Germany, October 8-19, 1979, volume 84 of Lecture Notes in Computer Science, pages 1-19. Springer, 1979. URL: https://doi.org/10.1007/3-540-10001-6_21.
  23. Charles Rackoff. The covering and boundedness problems for vector addition systems. Theor. Comput. Sci., 6:223-231, 1978. URL: https://doi.org/10.1016/0304-3975(78)90036-1.
  24. Philippe Schnoebelen. Revisiting Ackermann-hardness for lossy counter machines and reset Petri nets. In Petr Hlinený and Antonín Kucera, editors, Mathematical Foundations of Computer Science 2010, 35th International Symposium, MFCS 2010, Brno, Czech Republic, August 23-27, 2010. Proceedings, volume 6281 of Lecture Notes in Computer Science, pages 616-628. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-15155-2_54.
  25. Ferucio Laurentiu Tiplea, Corina Bocaneala, and Raluca Chirosca. On the complexity of deciding soundness of acyclic workflow nets. IEEE Trans. Syst. Man Cybern. Syst., 45(9):1292-1298, 2015. URL: https://doi.org/10.1109/TSMC.2015.2394735.
  26. Ferucio Laurentiu Tiplea and Dan C. Marinescu. Structural soundness of workflow nets is decidable. Inf. Process. Lett., 96(2):54-58, 2005. URL: https://doi.org/10.1016/j.ipl.2005.06.002.
  27. Rüdiger Valk. Self-modifying nets, a natural extension of Petri nets. In Giorgio Ausiello and Corrado Böhm, editors, Automata, Languages and Programming, Fifth Colloquium, Udine, Italy, July 17-21, 1978, Proceedings, volume 62 of Lecture Notes in Computer Science, pages 464-476. Springer, 1978. URL: https://doi.org/10.1007/3-540-08860-1_35.
  28. Wil M. P. van der Aalst. The application of Petri nets to workflow management. J. Circuits Syst. Comput., 8(1):21-66, 1998. URL: https://doi.org/10.1142/S0218126698000043.
  29. Wil M. P. van der Aalst, Kees M. van Hee, Arthur H. M. ter Hofstede, Natalia Sidorova, H. M. W. Verbeek, Marc Voorhoeve, and Moe Thandar Wynn. Soundness of workflow nets with reset arcs. Trans. Petri Nets Other Model. Concurr., 3:50-70, 2009. URL: https://doi.org/10.1007/978-3-642-04856-2_3.
  30. Wil M. P. van der Aalst, Kees M. van Hee, Arthur H. M. ter Hofstede, Natalia Sidorova, H. M. W. Verbeek, Marc Voorhoeve, and Moe Thandar Wynn. Soundness of workflow nets: classification, decidability, and analysis. Formal Aspects Comput., 23(3):333-363, 2011. URL: https://doi.org/10.1007/s00165-010-0161-4.