Reversible Computation vs. Reversibility in Petri Nets

  • Kamila Barylska
  • Maciej Koutny
  • Łukasz MikulskiEmail author
  • Marcin Piątkowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9720)


Petri nets are a general formal model of concurrent systems which supports both action-based and state-based modelling and reasoning. One of important behavioural properties investigated in the context of Petri nets has been reversibility, understood as the possibility of returning to the initial marking from any reachable net marking. Thus reversibility in Petri nets is a global property. Reversible computation, on the other hand, is typically a local mechanism using which a system can undo some of the executed actions. This paper is concerned with the modelling of reversible computation within Petri nets. A key idea behind the proposed construction is to add ‘reverse’ versions of selected transitions. Since such a modification can severely impact on the behavior of the system, it is crucial, in particular, to be able to determine whether the modified system has a similar set of states as the original one. We first prove that the problem of establishing whether the two nets have the same reachable markings is undecidable even in the restricted case discussed in this paper. We then show that the problem of checking whether the reachability sets of the two nets cover the same markings is decidable.


Petri net Reversibility Reversible computation Decidability 



We would like to thank the anonymous reviewers for their remarks which allowed us to improve the presentation of the paper. This work was supported by the EU COST Action IC1405, and by the Polish National Science Center (grant No. 2013/09/D/ST6/03928).


  1. 1.
    Araki, T., Kasami, T.: Decidable problems on the strong connectivity of Petri net reachability sets. Theoret. Comput. Sci. 4(1), 99–119 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Berry, G., Boudol, G.: The chemical abstract machine. Theoret. Comput. Sci. 96(1), 217–248 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Best, E., Desel, J., Esparza, J.: Traps characterize home states in free choice systems. Theoret. Comput. Sci. 101, 161–176 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Best, E., Esparza, J.: Existence of home states in Petri nets is decidable. Inf. Process. Lett. 116(6), 423–427 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Best, E., Schlachter, U.: Analysis of Petri nets and transition systems. In: Proceedings of 8th Interaction and Concurrency Experience (ICE 2015), EPTCS, vol. 189, pp. 53–67 (2015)Google Scholar
  6. 6.
    Best, E., Klaus, V.: Free choice systems have home states. Acta Informatica 21, 89–100 (1984)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cardelli, L., Laneve, C.: Reversible structures. In: Fages, F. (ed.) Proceedings of 9th International Computational Methods in Systems Biology (CMSB 2011), pp. 131–140. ACM (2011)Google Scholar
  8. 8.
    Danos, V., Krivine, J.: Reversible communicating systems. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 292–307. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Danos, V., Krivine, J.: Transactions in RCCS. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 398–412. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Danos, V., Krivine, J., Sobocinski, P.: General reversibility. Electron. Notes Theoret. Comput. Sci. 175(3), 75–86 (2007)CrossRefzbMATHGoogle Scholar
  11. 11.
    de Frutos Escrig, D., Johnen, C.: Decidability of home space property. Technical report 503, Laboratoire de Recherche en Informatique, Université de Paris-Sud (1989)Google Scholar
  12. 12.
    Desel, J., Esparza, J.: Reachability in cyclic extended free-choice systems. Theoret. Comput. Sci. 114, 93–118 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Finkel, A.: The minimal coverability graph for Petri nets. In: Rozenberg, G. (ed.) Petri Nets 1993. LNCS, vol. 674, pp. 210–243. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  14. 14.
    Michael, H.: Decidability questions for Petri nets. Technical report TR-161, MIT Laboratory for Computer Science (1976)Google Scholar
  15. 15.
    Michael, H.: Petri net languages. Technical report TR 159, MIT Laboratory for Computer Science (1976)Google Scholar
  16. 16.
    Hujsa, T., Delosme, J.-M., Munier-Kordon, A.: On the reversibility of live equal-conflict Petri nets. In: Devillers, R., Valmari, A. (eds.) PETRI NETS 2015. LNCS, vol. 9115, pp. 234–253. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  17. 17.
    Karp, R., Miller, R.: Parallel program schemata. J. Comput. Syst. Sci. 3, 147–195 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kezić, D., Perić, N., Petrović, I.: An algorithm for deadlock prevention based on iterative siphon control of Petri net. Automatika 47, 19–30 (2006)Google Scholar
  19. 19.
    Lanese, I., Mezzina, C.A., Stefani, J.-B.: Reversing higher-order Pi. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 478–493. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  20. 20.
    Özkan, H.A., Aybar, A.: A reversibility enforcement approach for Petri nets using invariants. WSEAS Trans. Syst. 7, 672–681 (2008)Google Scholar
  21. 21.
    Phillips, I., Ulidowski, I.: Reversing algebraic process calculi. J. Log. Algebr. Program. 73(1–2), 70–96 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Phillips, I., Ulidowski, I.: Reversibility and asymmetric conflict in event structures. J. Log. Algebr. Methods Program. 84(6), 781–805 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Phillips, I., Ulidowski, I., Yuen, S.: A reversible process calculus and the modelling of the ERK signalling pathway. In: Glück, R., Yokoyama, T. (eds.) RC 2012. LNCS, vol. 7581, pp. 218–232. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  24. 24.
    Recalde, L., Teruel, E., Silva, M.: Modeling and analysis of sequential processes that cooperate through buffers. IEEE Trans. Robot. Autom. 14(2), 267–277 (1998)CrossRefGoogle Scholar
  25. 25.
    Reisig, W.: Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science, vol. 4. Springer, Berlin (1985)CrossRefzbMATHGoogle Scholar
  26. 26.
    Teruel, E., Silva, M., Colom, J.M.: Choice-free Petri nets: a model for deterministic concurrent systems with bulk services and arrivals. IEEE Trans. Syst. Man Cybern. Part A 27, 73–83 (1997)CrossRefGoogle Scholar
  27. 27.
    Teruel, E., Silva, M.: Liveness and home states in equal conflict systems. PETRI NETS 1993. LNCS, vol. 691, pp. 415–432. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  28. 28.
    Vogler, W.: Live and bounded free choice nets have home states. Petri Net Newslett. 32, 18–21 (1989)Google Scholar
  29. 29.
    Wang, P., Ding, Z., Chai, H.: An algorithm for generating home states of Petri nets. J. Comput. Inf. Syst. 12(7), 4225–4232 (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Kamila Barylska
    • 1
  • Maciej Koutny
    • 2
  • Łukasz Mikulski
    • 1
    Email author
  • Marcin Piątkowski
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceNicolaus Copernicus UniversityToruńPoland
  2. 2.School of Computing ScienceNewcastle UniversityNewcastle upon TyneUK

Personalised recommendations