The Iterated Restricted Immediate Snapshot Model

  • Sergio Rajsbaum
  • Michel Raynal
  • Corentin Travers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


In the Iterated Immediate Snapshot model (\({\mathit{IIS}}\)) the memory consists of a sequence of one-shot Immediate Snapshot (\(\mathit{IS}\)) objects. Processes access the sequence of \(\mathit{IS}\) objects, one-by-one, asynchronously, in a wait-free manner; any number of processes can crash. Its interest lies in the elegant recursive structure of its runs, hence of the ease to analyze it round by round. In a very interesting way, Borowsky and Gafni have shown that the \({\mathit{IIS}}\) model and the read/write model are equivalent for the wait-free solvability of decision tasks.

This paper extends the benefits of the \(\mathit{IIS}\) model to partially synchronous systems. Given a shared memory model enriched with a failure detector, what is an equivalent \(\mathit{IIS}\) model? The paper shows that an elegant way of capturing the power of a failure detector and other partially synchronous systems in the \({\mathit{IIS}}\) model is by restricting appropriately its set of runs, giving rise to the Iterated Restricted Immediate Snapshot model (\(\mathit{IRIS}\)).


Shared Memory Global State Correct Process Failure Detector Asynchronous System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Afek, Y., Attiya, H., Dolev, D., Gafni, E., Merritt, M., Shavit, N.: Atomic Snapshots of Shared Memory. J. ACM 40(4), 873–890 (1993)zbMATHCrossRefGoogle Scholar
  2. 2.
    Attiya, H., Bar-Noy, A., Dolev, D.: Sharing Memory Robustly in Message Passing Systems. J. ACM 42(1), 124–142 (1995)zbMATHCrossRefGoogle Scholar
  3. 3.
    Awerbuch, B.: Complexity of network synchronization. J. ACM 32, 804–823 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations, and Advanced Topics. Wiley, Chichester (2004)Google Scholar
  5. 5.
    Borowsky, E., Gafni, E.: Immediate Atomic Snapshots and Fast Renaming. In: Proc. of PODC 1993, pp. 41–51 (1993)Google Scholar
  6. 6.
    Borowsky, E., Gafni, E.: Generalized FLP Impossibility Results for t-Resilient Asynchronous Computations. In: Proc. 25th ACM STOC, pp. 91–100 (1993)Google Scholar
  7. 7.
    Borowsky, E., Gafni, E.: A Simple Algorithmically Reasoned Characterization of Wait-free Computations. In: Proc. 16th ACM PODC, pp. 189–198 (1997)Google Scholar
  8. 8.
    Chandra, T., Toueg, S.: Unreliable Failure Detectors for Reliable Distributed Systems. J. ACM 43(2), 225–267 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Chandra, T., Hadzilacos, V., Toueg, S.: The Weakest Failure Detector for Solving Consensus. J. ACM 43(4), 685–722 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Chaudhuri, S.: More Choices Allow More Faults: Set Consensus Problems in Totally Asynchronous Systems. Information and Computation 105, 132–158 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Dwork, C., Lynch, N., Stockmeyer, L.: Consensus in the Presence of Partial Synchrony. J. ACM 35(2), 288–323 (1988)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Gafni, E.: Round-by-round Fault Detectors: Unifying Synchrony and Asynchrony. In: Proc. 17th ACM Symp. on Principles of Distributed Computing, pp. 143–152 (1998)Google Scholar
  13. 13.
    Gafni, E., Rajsbaum, S., Herlihy, M.: Subconsensus Tasks: Renaming is Weaker than Set Agreement. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 329–338. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Herlihy, M., Penso, L.D.: Tight Bounds for k-Set Agreement with Limited Scope Accuracy Failure Detectors. Distributed Computing 18(2), 157–166 (2005)CrossRefGoogle Scholar
  15. 15.
    Herlihy, M.P., Rajsbaum, S., Tuttle, M.: Unifying Synchronous and Asynchronous Message-Passing Models. In: Proc. 17th ACM PODC, pp. 133–142 (1998)Google Scholar
  16. 16.
    Herlihy, M., Shavit, N.: The Topological Structure of Asynchronous Computability. J. ACM 46(6), 858–923 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Keidar, I., Shraer, A.: Timeliness, Failure-detectors, and Consensus Performance. In: Proc. 25th ACM PODC, pp. 169–178 (2006)Google Scholar
  18. 18.
    Mostefaoui, A., Rajsbaum, S., Raynal, M., Travers, C.: Irreducibility and Additivity of Set Agreement-oriented Failure Detector Classes. In: Proc. PODC 2006, pp. 153–162 (2006)Google Scholar
  19. 19.
    Rajsbaum, S., Raynal, M., Travers, C.: Failure Detectors as Schedulers. Tech Report # 1838, IRISA, Université de Rennes, France (2007)Google Scholar
  20. 20.
    Rajsbaum, S., Raynal, M., Travers, C.: The Iterated Restricted Immediate Snapshot Model. Tech Report # 1874, IRISA, Université de Rennes, France (2007)Google Scholar
  21. 21.
    Saks, M., Zaharoglou, F.: Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge. SIAM Journal on Computing 29(5), 1449–1483 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Völzer, H.: On Conspiracies and Hyperfairness in Distributed Computing. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 33–47. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  23. 23.
    Yang, J., Neiger, G., Gafni, E.: Structured Derivations of Consensus Algorithms for Failure Detectors. In: Proc. 17th ACM PODC, pp. 297–308 (1998)Google Scholar
  24. 24.
    Zieliński, P.: Anti-Omega: the Weakest Failure Detector for Set Agreement. Tech Rep # 694, University of Cambridge (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sergio Rajsbaum
    • 1
  • Michel Raynal
    • 2
  • Corentin Travers
    • 3
  1. 1.Instituto de MatemáticasUNAMMexico
  2. 2.IRISARennes CedexFrance
  3. 3.Facultad de InformáticaUPMMadridSpain

Personalised recommendations