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Reversible Computation vs. Reversibility in Petri Nets

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

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.

Keywords

Petri net Reversibility Reversible computation Decidability 

Notes

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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

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

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