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Reversible Computation vs. Reversibility in Petri Nets

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Reversible Computation (RC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9720))

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Abstract

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.

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Notes

  1. 1.

    The mirror of \(t_1t_2\ldots t_k\in T_A^*\) is \(t_1't_2'\ldots t_k' \in T_B^*\), and vice versa.

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Acknowledgements

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).

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, Toruń, Poland

    Kamila Barylska, Łukasz Mikulski & Marcin Piątkowski

  2. School of Computing Science, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK

    Maciej Koutny

Authors
  1. Kamila Barylska
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  2. Maciej Koutny
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  3. Łukasz Mikulski
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  4. Marcin Piątkowski
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Correspondence to Łukasz Mikulski .

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Editors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Simon Devitt

  2. University of Bologna/Inria, Bologna, Italy

    Ivan Lanese

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Barylska, K., Koutny, M., Mikulski, Ł., Piątkowski, M. (2016). Reversible Computation vs. Reversibility in Petri Nets. In: Devitt, S., Lanese, I. (eds) Reversible Computation. RC 2016. Lecture Notes in Computer Science(), vol 9720. Springer, Cham. https://doi.org/10.1007/978-3-319-40578-0_7

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  • DOI: https://doi.org/10.1007/978-3-319-40578-0_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40577-3

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