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Relating Reversible Petri Nets and Reversible Event Structures, Categorically

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Formal Techniques for Distributed Objects, Components, and Systems (FORTE 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13910))

Abstract

Causal nets (CNs) are Petri nets where causal dependencies are modelled via inhibitor arcs. They play the role of occurrence nets when representing the behaviour of a concurrent and distributed system, even when reversibility is considered. In this paper we extend CNs to account also for asymmetric conflicts and study (i) how this kind of nets, and their reversible versions, can be turned into a category; and (ii) their relation with the categories of reversible asymmetric event structures.

This work has been supported by the Italian MUR PRIN 2020 project NiRvAna, the French ANR project ANR-18-CE25-0007 DCore, the INdAM-GNCS project CUP_E55F22000270001 Proprietà Qualitative e Quantitative di Sistemi Reversibili, and the European Union - NextGenerationEU program Research and Innovation Program PE00000014 SEcurity and RIghts in the CyberSpace (SERICS), projects Secure and TRaceable Identities in Distributed Environments (STRIDE) and Securing softWare frOm first PrincipleS (SWOPS), the EU H2020 RISE programme under the Marie Skłodowska-Curie grant agreement 778233, UBACyT projects 20020170100544BA and 20020170100086BA.

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Notes

  1. 1.

    Definition 4 differs in style from the one in [20] where < and \(\prec \) are glued in one relation as also are \(\nearrow \) and \(\lhd \). We explicitly require \((E,\prec \!\!\prec , \nearrow )\) to be an aes instead of restating conditions. The correspondence is straightforward.

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Authors and Affiliations

  1. ICC - Universidad de Buenos Aires, Buenos Aires, Argentina

    Hernán Melgratti

  2. Dipartimento di Scienze Pure e Applicate, Università di Urbino, Urbino, Italy

    Claudio Antares Mezzina

  3. Dipartimento di Matematica e Informatica, Università di Cagliari, Cagliari, Italy

    G. Michele Pinna

Authors
  1. Hernán Melgratti
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  2. Claudio Antares Mezzina
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  3. G. Michele Pinna
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Corresponding authors

Correspondence to Hernán Melgratti , Claudio Antares Mezzina or G. Michele Pinna .

Editor information

Editors and Affiliations

  1. University of Twente, Enschede, The Netherlands

    Marieke Huisman

  2. NOVA School of Science and Technology and NOVA LINCS, Caparica, Portugal

    António Ravara

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Melgratti, H., Mezzina, C.A., Pinna, G.M. (2023). Relating Reversible Petri Nets and Reversible Event Structures, Categorically. In: Huisman, M., Ravara, A. (eds) Formal Techniques for Distributed Objects, Components, and Systems. FORTE 2023. Lecture Notes in Computer Science, vol 13910. Springer, Cham. https://doi.org/10.1007/978-3-031-35355-0_13

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  • DOI: https://doi.org/10.1007/978-3-031-35355-0_13

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