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Wait-freedom with advice

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Abstract

We motivate and propose a new way of thinking about failure detectors which allows us to define what it means to solve a distributed task wait-free using a failure detector. In our model, the system is composed of computation processes that obtain inputs and are supposed to produce outputs and synchronization processes that are subject to failures and can query a failure detector. Under the condition that correct (never failing) synchronization processes take sufficiently many steps, they provide the computation processes with enough advice to solve the given task wait-free: every computation process outputs in a finite number of its own steps, regardless of the behavior of other computation processes. Every task can thus be characterized by the weakest failure detector that allows for solving it, and we show that every such failure detector captures a form of set agreement. We then obtain a complete classification of tasks, including ones that evaded comprehensible characterization so far, such as renaming or weak symmetry breaking.

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Notes

  1. Informally, \(\mathcal {D}\) is the weakest failure detector to solve a task \(T\) if it (1) solves \(T\) and (2) can be deduced from any failure detector that solves \(T\).

  2. Note that all tasks can be solved \(1\)-concurrently.

  3. For some values of \(j\) and \(k\), however, the question of the maximal tolerated concurrency of \((j,j+k-1)\)-renaming is still open [11].

  4. In other words, point contention [6] in the run with respect to \(C\)-processes does not exceed \(k\).

  5. A trivial failure detector always outputs \(\bot \).

  6. Recall that, informally, in a solution of a colorless task, a process is free to adopt the input or the output value of any other participating process.

  7. The procedure is similar to the corridor-based depth-first search simulation of [26].

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Acknowledgments

The work of Carole Delporte-Gallet and Hugues Fauconnier is supported by the ANR SIMI2 DISPLEXITY.

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Authors and Affiliations

  1. University Paris Diderot, Paris, France

    Carole Delporte-Gallet & Hugues Fauconnier

  2. UCLA, Los Angeles, CA, USA

    Eli Gafni

  3. Télécom ParisTech, Paris, France

    Petr Kuznetsov

Authors
  1. Carole Delporte-Gallet
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  2. Hugues Fauconnier
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  3. Eli Gafni
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  4. Petr Kuznetsov
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Correspondence to Carole Delporte-Gallet.

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Delporte-Gallet, C., Fauconnier, H., Gafni, E. et al. Wait-freedom with advice. Distrib. Comput. 28, 3–19 (2015). https://doi.org/10.1007/s00446-014-0231-6

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