t-Resilient Immediate Snapshot Is Impossible

  • Carole Delporte
  • Hugues Fauconnier
  • Sergio Rajsbaum
  • Michel Raynal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9988)


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.


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 


  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)CrossRefMATHGoogle Scholar
  2. 2.
    Anderson, J.: Multi-writer composite registers. Distrib. Comput. 7(4), 175–195 (1994)CrossRefGoogle Scholar
  3. 3.
    Attiya, H., Bar-Noy, A., Dolev, D., Peleg, D., Reischuk, R.: Renaming in an asynchronous environment. J. ACM 37(3), 524–548 (1990)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations and Advanced Topics, 2nd edn. Wiley-Interscience, New York (2004). 414 pagesCrossRefMATHGoogle Scholar
  5. 5.
    Borowsky E., Gafni E.: Immediate atomic snapshots and fast renaming. In: Proceedings of the 12th ACM Symposium on Principles of Distributed Computing (PODC 1993), pp. 41–50 (1993)Google Scholar
  6. 6.
    Borowsky E. and Gafni E., Generalized FLP impossibility results for \(t\)-resilient asynchronous computations. In: Proceedings of the 25th ACM Symposium on Theory of Computation (STOC 1993), California, USA, pp. 91–100 (1993)Google Scholar
  7. 7.
    Borowsky E., Gafni E.: A simple algorithmically reasoned characterization of wait-free computations. In: Proceedings of the 16th ACM Symposium on Principles of Distributed Computing (PODC 1997), pp. 189–198. ACM Press (1997)Google Scholar
  8. 8.
    Borowsky, E., Gafni, E., Lynch, N., Rajsbaum, S.: The BG distributed simulation algorithm. Distrib. Comput. 14, 127–146 (2001)CrossRefGoogle Scholar
  9. 9.
    Castañeda, A., Rajsbaum, S., Raynal, M.: Specifying concurrent problems: beyond linearizability and up to tasks. In: Moses, Y. (ed.) DISC 2015. LNCS, vol. 9363, pp. 420–435. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48653-5_28 CrossRefGoogle Scholar
  10. 10.
    Chandra, T., Hadzilacos, V., Toueg, S.: The weakest failure detector for solving consensus. J. ACM 43(4), 685–722 (1996)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Chaudhuri, S.: More choices allow more faults: set consensus problems in totally asynchronous systems. Inf. Comput. 105(1), 132–158 (1993)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Delporte, C., Fauconnier, H., Rajsbaum, S., Raynal, M.: \(t\)-resilient immediate snapshot is impossible. Technical report 2036, IRISA, Université de Rennes (F): http://hal.inria.fr/hal-01313556
  13. 13.
    Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Gafni E., Kuznetsov P., and Manolescu C., A generalized asynchronous computability theorem. In: Proceedings of the 33th ACM Symposium on Principles of Distributed Computing (PODC 1994), pp. 222–231. ACM Press (2014)Google Scholar
  15. 15.
    Gafni, E., Rajsbaum, S.: Recursion in distributed computing. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds.) SSS 2010. LNCS, vol. 6366, pp. 362–376. Springer, Heidelberg (2010). doi:10.1007/978-3-642-16023-3_30 CrossRefGoogle Scholar
  16. 16.
    Herlihy, M.P.: Wait-free synchronization. ACM Trans. Program. Lang. Syst. 13(1), 124–149 (1991)CrossRefGoogle Scholar
  17. 17.
    Herlihy, M.P., Kozlov, D., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Morgan Kaufmann/Elsevier, New York (2014). 336 pages. ISBN 9780124045781MATHGoogle Scholar
  18. 18.
    Herlihy, M.P., Luchangco, V., Moir, M.: Obstruction-free synchronization: double-ended queues as an example. In: Proceedings of the 23th International IEEE Conference on Distributed Computing Systems (ICDCS 2003), pp. 522–529. IEEE Press (2003)Google Scholar
  19. 19.
    Herlihy, M., Rajsbaum, S., Raynal, M.: Power and limits of distributed computing shared memory models. Theor. Comput. Sci. 509, 3–24 (2013)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Herlihy, M.P., Shavit, N.: A simple constructive computability theorem for wait-free computation. In: Proceedings of the 26th ACM Symposium on Theory of Computing (STOC 1994), pp. 243–252. ACM Press (1994)Google Scholar
  21. 21.
    Herlihy, M.P., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Herlihy, M.P., Wing, J.M.: Linearizability: a correctness condition for concurrent objects. ACM Trans. Programm. Lang. Syst. 12(3), 463–492 (1990)CrossRefGoogle Scholar
  23. 23.
    Lamport, L.: On interprocess communication, Part I: basic formalism. Distrib. Comput. 1(2), 77–85 (1986)CrossRefMATHGoogle Scholar
  24. 24.
    Lo, W.-K., Hadzilacos, V.: Using failure detectors to solve consensus in asynchronous shared-memory systems. In: Tel, G., Vitányi, P. (eds.) WDAG 1994. LNCS, vol. 857, pp. 280–295. Springer, Heidelberg (1994). doi:10.1007/BFb0020440 CrossRefGoogle Scholar
  25. 25.
    Loui, M., Abu-Amara, H.: Memory requirements for agreement among unreliable asynchronous processes. Adv. Comput. Res. 4, 163–183 (1987)MathSciNetGoogle Scholar
  26. 26.
    Neiger G., Set-linearizability. In: Brief Announcement in Proceedings of the 13th ACM Symposium on Principles of Distributed Computing (PODC 1994), p. 396. ACM Press (1994)Google Scholar
  27. 27.
    Rajsbaum, S.: Iterated shared memory models. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 407–416. Springer, Heidelberg (2010). doi:10.1007/978-3-642-12200-2_36 CrossRefGoogle Scholar
  28. 28.
    Rajsbaum, S., Raynal, M.: An introductory tutorial to concurrency-related distributed recursion. Bull. Eur. Assoc. TCS 111, 57–75 (2013)MathSciNetGoogle Scholar
  29. 29.
    Rajsbaum, S., Raynal, M., Travers, C.: The iterated restricted immediate snapshot model. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 487–497. Springer, Heidelberg (2008). doi:10.1007/978-3-540-69733-6_48 CrossRefGoogle Scholar
  30. 30.
    Rajsbaum, S., Raynal, M., Travers, C.: An impossibility about failure detectors in the iterated immediate snapshot model. Inf. Process. Lett. 108(3), 160–164 (2008)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Raynal, M.: Concurrent Programming: Algorithms, Principles and Foundations. Springer, Heidelberg (2013). 515 pages. ISBN 978-3-642-32026-2CrossRefMATHGoogle Scholar
  32. 32.
    Raynal, M., Stainer, J.: Increasing the power of the iterated immediate snapshot model with failure detectors. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 231–242. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31104-8_20 CrossRefGoogle Scholar
  33. 33.
    Saks, M., Zaharoglou, F.: Wait-free \(k\)-set agreement is impossible: the topology of public knowledge. SIAM J. Comput. 29(5), 1449–1483 (2000)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Taubenfeld, G.: Synchronization Algorithms and Concurrent Programming. Pearson Prentice-Hall, Upper Saddle River (2006). 423 pages. ISBN 0-131-97259-6Google Scholar

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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