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Invited Paper: Time Is Not a Healer, but It Sure Makes Hindsight 20:20

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Stabilization, Safety, and Security of Distributed Systems (SSS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14310))

Abstract

In the 1980s, three related impossibility results emerged in the field of distributed computing. First, Fischer, Lynch, and Paterson demonstrated that deterministic consensus is unattainable in an asynchronous message-passing system when a single process may crash-stop. Subsequently, Loui and Abu-Amara showed the infeasibility of achieving consensus in asynchronous shared-memory systems, given the possibility of one crash-stop failure. Lastly, Santoro and Widmayer established the impossibility of consensus in synchronous message-passing systems with a single process per round experiencing send-omission faults.

In this paper, we revisit these seminal results. First, we observe that all these systems are equivalent in the sense of implementing each other. Then, we prove the impossibility of consensus in the synchronous system of Santoro and Widmayer, which is the easiest to reason about. Taking inspiration from Volzer’s proof pearl and from the Borowski-Gafni simulation, we obtain a remarkably simple proof.

We believe that a contemporary pedagogical approach to teaching these results should first address the equivalence of the systems before proving the consensus impossibility within the system where the result is most evident.

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Notes

  1. 1.

    \(n>2\) is required for the ABD shared-memory simulation algorithm and by the get-core algorithm.

  2. 2.

    See Sect. 2.1 for a discussion of colorless tasks.

  3. 3.

    This is an instance of the following first-order logic tautology: \(\exists y. \forall x .P(x,y)\rightarrow \forall x. \exists y . P(x,y)\).

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Author information

Authors and Affiliations

  1. University of California, Los Angeles, USA

    Eli Gafni

  2. Stellar Development Foundation, San Francisco, USA

    Giuliano Losa

Authors
  1. Eli Gafni
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  2. Giuliano Losa
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Correspondence to Giuliano Losa .

Editor information

Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be'er-Sheva, Israel

    Shlomi Dolev

  2. New Jersey Institute of Technology, Newark, NJ, USA

    Baruch Schieber

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Gafni, E., Losa, G. (2023). Invited Paper: Time Is Not a Healer, but It Sure Makes Hindsight 20:20. In: Dolev, S., Schieber, B. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2023. Lecture Notes in Computer Science, vol 14310. Springer, Cham. https://doi.org/10.1007/978-3-031-44274-2_6

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  • DOI: https://doi.org/10.1007/978-3-031-44274-2_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-44273-5

  • Online ISBN: 978-3-031-44274-2

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