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Causal Reversibility Implies Time Reversibility

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Quantitative Evaluation of Systems (QEST 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14287))

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Abstract

Several notions of reversibility exist in the literature. On the one hand, causal reversibility establishes that an action can be undone provided that all of its consequences have been undone already, thereby making it possible to bring a system back to a past consistent state. On the other hand, time reversibility stipulates that the stochastic behavior of a system remains the same when the direction of time is reversed, which supports efficient performance evaluation. In this paper we show that causal reversibility is a sufficient condition for time reversibility. The study is conducted on extended labeled transition systems. Firstly, they include a forward and a backward transition relations obeying the loop property. Secondly, their transitions feature an independence relation as well as rates for their exponentially distributed random durations. Our result can thus be smoothly applied to concurrent and distributed models, calculi, and languages that account for performance aspects.

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Data Availability Statement

The machine-checkable proof of the result in Sect. 3 has been accepted by the QEST 2023 artifact evaluation committee and is available at https://github.com/sacerdot/Causal2TimedFormalization.

Notes

  1. 1.

    It is often called causal-consistent reversibility in the literature after [18].

  2. 2.

    It was called coinitial propagation of independence (CPI) in [22].

  3. 3.

    A property called unique transitions (UT) in [22].

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Acknowledgments

This work has been supported by the Italian PRIN 2020 project NiRvAna – Noninterference and Reversibility Analysis in Private Blockchains, the French ANR-18-CE25-0007 project DCore – Causal Debugging for Concurrent Systems, and the INdAM-GNCS E53C22001930001 project RISICO – Reversibilità in Sistemi Concorrenti: Analisi Quantitative e Funzionali.

Author information

Authors and Affiliations

  1. Department of Pure and Applied Sciences, University of Urbino, Urbino, Italy

    Marco Bernardo & Claudio A. Mezzina

  2. Focus Team, University of Bologna & INRIA, Bologna, Italy

    Ivan Lanese

  3. Department of Environmental Sciences, Informatics and Statistics, University Ca’ Foscari, Venice, Italy

    Andrea Marin & Sabina Rossi

  4. Department of Informatics – Science and Engineering, University of Bologna, Bologna, Italy

    Claudio Sacerdoti Coen

Authors
  1. Marco Bernardo
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  2. Ivan Lanese
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  3. Andrea Marin
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  4. Claudio A. Mezzina
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  5. Sabina Rossi
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  6. Claudio Sacerdoti Coen
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Correspondence to Marco Bernardo .

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Editors and Affiliations

  1. Radboud University Nijmegen, Nijmegen, The Netherlands

    Nils Jansen

  2. IMT Lucca, Lucca, Italy

    Mirco Tribastone

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Bernardo, M., Lanese, I., Marin, A., Mezzina, C.A., Rossi, S., Sacerdoti Coen, C. (2023). Causal Reversibility Implies Time Reversibility. In: Jansen, N., Tribastone, M. (eds) Quantitative Evaluation of Systems. QEST 2023. Lecture Notes in Computer Science, vol 14287. Springer, Cham. https://doi.org/10.1007/978-3-031-43835-6_19

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  • DOI: https://doi.org/10.1007/978-3-031-43835-6_19

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