t-Resilient Immediate Snapshot Is Impossible

  • Carole Delporte
  • Hugues Fauconnier
  • Sergio Rajsbaum
  • Michel Raynal
Conference paper

DOI: 10.1007/978-3-319-48314-6_12

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9988)
Cite this paper as:
Delporte C., Fauconnier H., Rajsbaum S., Raynal M. (2016) t-Resilient Immediate Snapshot Is Impossible. In: Suomela J. (eds) Structural Information and Communication Complexity. SIROCCO 2016. Lecture Notes in Computer Science, vol 9988. Springer, Cham

Abstract

An immediate snapshot object is a high level communication object, built on top of a read/write distributed system in which all except one processes may crash. It allows each process to write a value and obtains a set of pairs (process id, value) such that, despite process crashes and asynchrony, the sets obtained by the processes satisfy noteworthy inclusion properties.

Considering an n-process model in which up to t processes are allowed to crash (t-crash system model), this paper is on the construction of t-resilient immediate snapshot objects. In the t-crash system model, a process can obtain values from at least \((n-t)\) processes, and, consequently, t-immediate snapshot is assumed to have the properties of the basic \((n-1)\)-resilient immediate snapshot plus the additional property stating that each process obtains values from at least \((n-t)\) processes. The main result of the paper is the following. While there is a (deterministic) \((n-1)\)-resilient algorithm implementing the basic \((n-1)\)-immediate snapshot in an \((n-1)\)-crash read/write system, there is no t-resilient algorithm in a t-crash read/write model when \(t\in [1\ldots (n-2)]\). This means that, when \(t<n-1\), the notion of t-resilience is inoperative when one has to implement t-immediate snapshot for these values of t: the model assumption “at most \(t<n-1\) processes may crash” does not provide us with additional computational power allowing for the design of a genuine t-resilient algorithm (genuine meaning that such an algorithm would work in the t-crash model, but not in the \((t+1)\)-crash model). To show these results, the paper relies on well-known distributed computing agreement problems such as consensus and k-set agreement.

Keywords

Asynchronous system Atomic read/write register Consensus Distributed computability Immediate snapshot Impossibility Iterated model k-Set Agreement Linearizability Process crash failure Snapshot object t-Resilience Wait-freedom 

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Carole Delporte
    • 1
  • Hugues Fauconnier
    • 1
  • Sergio Rajsbaum
    • 2
  • Michel Raynal
    • 3
  1. 1.IRIF/GANG, Université Paris DiderotParisFrance
  2. 2.Instituto de MatemáticasUNAMMéxico D.F.Mexico
  3. 3.IUF, IRISA (Université de Rennes)RennesFrance

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