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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

Funding

  • Chistikov, Dmitry: Supported in part by the Engineering and Physical Sciences Research Council [EP/X03027X/1].
  • Czerwiński, Wojciech: Supported by the ERC grant INFSYS, agreement no. 950398.
  • Hofman, Piotr: Supported by the ERC grant INFSYS, agreement no. 950398.
  • Mazowiecki, Filip: Supported by the ERC grant INFSYS, agreement no. 950398.
  • Sinclair-Banks, Henry: Supported by EPSRC Standard Research Studentship (DTP), grant number EP/T5179X/1.

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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