Abstract
In reversible computations one is interested in the development of mechanisms allowing to undo the effects of executed actions. The past research has been concerned mainly with reversing single actions. In this paper, we consider the problem of reversing the effect of the execution of groups of actions (steps).
Using Petri nets as a system model, we introduce concepts related to this new scenario, generalising notions used in the single action case. We then present a number of properties which arise in the context of reversing of steps of executed transitions in place/transition nets. We obtain both positive and negative results, showing that dealing with steps makes reversibility more involved than in the sequential case. In particular, we demonstrate that there is a crucial difference between reversing steps which are sets and those which are true multisets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Arcs labelled with the empty multiset will not be usually depicted.
- 2.
If \({ STS }\) and \({ STS }'\) are well-formed, then \(\psi \) is unique due to FD & REA.
- 3.
If \({ STS }\) is well-formed, then \({ STS }^{{ seq }}\), \({ STS }^{{ set }}\), and \({ STS }^{{ spike }}\) satisfy REA due to REA & SEQ.
- 4.
Note that \({ STS }|_{T'}\) may be not REA even for \({ STS }\) that is REA.
- 5.
Intuitively, each \(p_t\in P_p\) is a (suitably adjusted) copy of p.
References
Badouel, E., Darondeau, P.: Theory of regions. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 529–586. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-65306-6_22
Barylska, K., Best, E., Erofeev, E., Mikulski, Ł., Piątkowski, M.: Conditions for Petri net solvable binary words. ToPNoC 11, 137–159 (2016)
Barylska, K., Erofeev, E., Koutny, M., Mikulski, Ł., Piątkowski, M.: Reversing transitions in bounded Petri nets. Fundamenta Informaticae 157, 341–357 (2018)
Barylska, K., Koutny, M., Mikulski, Ł., Piątkowski, M.: Reversible computation vs. reversibility in Petri nets. Sci. Comput. Program. 151, 48–60 (2018)
Cardelli, L., Laneve, C.: Reversible structures. In: Proceedings of CMSB 2011, pp. 131–140 (2011)
Cohen, M.E.: Systems for financial and electronic commerce, 3 September 2013. US Patent 8,527,406
Danos, V., Krivine, J.: Reversible communicating systems. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 292–307. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28644-8_19
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). https://doi.org/10.1007/11539452_31
Danos, V., Krivine, J., Sobocinski, P.: General reversibility. Electr. Notes Theor. Comp. Sci. 175(3), 75–86 (2007)
Darondeau, P., Koutny, M., Pietkiewicz-Koutny, M., Yakovlev, A.: Synthesis of nets with step firing policies. Fundam. Inform. 94(3–4), 275–303 (2009)
de Frutos Escrig, D., Koutny, M., Mikulski, Ł.: An efficient characterization of petri net solvable binary words. In: Khomenko, V., Roux, O.H. (eds.) PETRI NETS 2018. LNCS, vol. 10877, pp. 207–226. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91268-4_11
Erofeev, E., Barylska, K., Mikulski, Ł., Piątkowski, M.: Generating all minimal Petri net unsolvable binary words. In: Proceedings of PSC 2016, pp. 33–46 (2016)
Esparza, J., Nielsen, M.: Decidability issues for Petri nets. BRICS Report Series 1(8), 1–25 (1994)
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, Cham (2015). https://doi.org/10.1007/978-3-319-19488-2_12
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). https://doi.org/10.1007/978-3-642-15375-4_33
Özkan, H.A., Aybar, A.: A reversibility enforcement approach for Petri nets using invariants. WSEAS Trans. Syst. 7, 672–681 (2008)
Phillips, I., Ulidowski, I.: Reversing algebraic process calculi. J. Logical Algebraic Program. 73(1–2), 70–96 (2007)
Phillips, I., Ulidowski, I.: Reversibility and asymmetric conflict in event structures. J. Logical Algebraic Meth. Program. 84(6), 781–805 (2015)
Reisig, W.: Understanding Petri Nets - Modeling Techniques, Analysis Methods, Case Studies. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-33278-4
De Vos, A.: Reversible Computing: Fundamentals, Quantum Computing, and Applications. Wiley (2011)
Acknowledgement
This research was supported by Cost Action IC1405. The first author was partially supported by the Spanish project TRACES (TIN2015-67522-C3-3), and by Comunidad de Madrid as part of the program S2018/TCS-4339 (BLOQUES-CM) co-funded by EIE Funds of the European Union.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
de Frutos Escrig, D., Koutny, M., Mikulski, Ł. (2019). Reversing Steps in Petri Nets. In: Donatelli, S., Haar, S. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2019. Lecture Notes in Computer Science(), vol 11522. Springer, Cham. https://doi.org/10.1007/978-3-030-21571-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-21571-2_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21570-5
Online ISBN: 978-3-030-21571-2
eBook Packages: Computer ScienceComputer Science (R0)