Impossibility of Strongly-Linearizable Message-Passing Objects via Simulation by Single-Writer Registers

Authors Hagit Attiya , Constantin Enea , Jennifer L. Welch



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Author Details

Hagit Attiya
  • Computer Science Department, Technion, Haifa, Israel
Constantin Enea
  • Université de Paris, IRIF, CNRS, France
Jennifer L. Welch
  • Texas A&M University, College Station, TX, USA

Acknowledgements

We thank the anonymous referees for helpful comments that improved the presentation of the paper.

Cite AsGet BibTex

Hagit Attiya, Constantin Enea, and Jennifer L. Welch. Impossibility of Strongly-Linearizable Message-Passing Objects via Simulation by Single-Writer Registers. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.DISC.2021.7

Abstract

A key way to construct complex distributed systems is through modular composition of linearizable concurrent objects. A prominent example is shared registers, which have crash-tolerant implementations on top of message-passing systems, allowing the advantages of shared memory to carry over to message-passing. Yet linearizable registers do not always behave properly when used inside randomized programs. A strengthening of linearizability, called strong linearizability, has been shown to preserve probabilistic behavior, as well as other "hypersafety" properties. In order to exploit composition and abstraction in message-passing systems, it is crucial to know whether there exist strongly-linearizable implementations of registers in message-passing. This paper answers the question in the negative: there are no strongly-linearizable fault-tolerant message-passing implementations of multi-writer registers, max-registers, snapshots or counters. This result is proved by reduction from the corresponding result by Helmi et al. The reduction is a novel extension of the BG simulation that connects shared-memory and message-passing, supports long-lived objects, and preserves strong linearizability. The main technical challenge arises from the discrepancy between the potentially minuscule fraction of failures to be tolerated in the simulated message-passing algorithm and the large fraction of failures that can afflict the simulating shared-memory system. The reduction is general and can be viewed as the inverse of the ABD simulation of shared memory in message-passing.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Computing methodologies → Distributed algorithms
  • Computing methodologies → Concurrent algorithms
  • Theory of computation → Concurrent algorithms
  • Theory of computation → Distributed algorithms
Keywords
  • Concurrent Objects
  • Message-passing systems
  • Strong linearizability
  • Impossibility proofs
  • BG simulation
  • Shared registers

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