Strong Equivalence Relations for Iterated Models

  • Zohir Bouzid
  • Eli Gafni
  • Petr Kuznetsov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8878)


The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical representation, has become standard for applying topological reasoning to distributed computing. Its modular structure makes it easier to analyze than the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS). It is known that AS and IIS are equivalent with respect to wait-free task computability: a distributed task is solvable in AS if and only if it is solvable in IIS. We observe, however, that this equivalence is not sufficient in order to explore solvability of tasks in sub-AS models (i.e. proper subsets of AS runs) or computability of long-lived objects, and a stronger equivalence relation is needed.

In this paper, we consider adversarial sub-AS and sub-IIS models specified by the sets of processes that can be correct in a model run. We show that AS and IIS are equivalent in a strong way: a (possibly long-lived) object is implementable in AS under a given adversary if and only if it is implementable in IIS under the same adversary. Therefore, the computability of any object in shared memory under an adversarial AS scheduler can be equivalently investigated in IIS.


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)CrossRefzbMATHGoogle Scholar
  2. 2.
    Borowsky, E., Gafni, E.: Generalized FLP impossibility result for t-resilient asynchronous computations. In: STOC, pp. 91–100. ACM Press (May 1993)Google Scholar
  3. 3.
    Borowsky, E., Gafni, E.: Immediate atomic snapshots and fast renaming. In: PODC, pp. 41–51. ACM Press, New York (1993)Google Scholar
  4. 4.
    Borowsky, E., Gafni, E.: A simple algorithmically reasoned characterization of wait-free computation (extended abstract). In: PODC, pp. 189–198 (1997)Google Scholar
  5. 5.
    Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Tielmann, A.: The disagreement power of an adversary. Distributed Computing 24(3-4), 137–147 (2011)CrossRefzbMATHGoogle Scholar
  6. 6.
    Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Gafni, E.: On the wait-free power of iterated-immediate-snapshots (1998), (unpublished manuscript)
  8. 8.
    Gafni, E.: Round-by-round fault detectors (extended abstract): Unifying synchrony and asynchrony. In: PODC, pp. 143–152 (1998)Google Scholar
  9. 9.
    Gafni, E.: The 0–1-exclusion families of tasks. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 246–258. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Gafni, E., Kuznetsov, P.: Turning adversaries into friends: Simplified, made constructive, and extended. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 380–394. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Gafni, E., Kuznetsov, P.: Relating \(\mathcal{L}\)-resilience and wait-freedom via hitting sets. In: Aguilera, M.K., Yu, H., Vaidya, N.H., Srinivasan, V., Choudhury, R.R. (eds.) ICDCN 2011. LNCS, vol. 6522, pp. 191–202. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Gafni, E., Kuznetsov, P., Manolescu, C.: A generalized asynchronous computability theorem. In: PODC (2014)Google Scholar
  13. 13.
    Gafni, E., Rajsbaum, S.: Distributed programming with tasks. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 205–218. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Gafni, E., Rajsbaum, S., Herlihy, M.P.: 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
  15. 15.
    Herlihy, M., Kozlov, D.N., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Morgan Kaufmann (2014)Google Scholar
  16. 16.
    Herlihy, M., Rajsbaum, S.: Simulations and reductions for colorless tasks. In: PODC, pp. 253–260 (2012)Google Scholar
  17. 17.
    Herlihy, M., Rajsbaum, S.: The topology of distributed adversaries. Distributed Computing 26(3), 173–192 (2013)CrossRefzbMATHGoogle Scholar
  18. 18.
    Herlihy, M., Shavit, N.: The asynchronous computability theorem for t-resilient tasks. In: STOC, pp. 111–120 (May 1993)Google Scholar
  19. 19.
    Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(2), 858–923 (1999)zbMATHMathSciNetGoogle Scholar
  20. 20.
    Herlihy, M., Shavit, N.: On the nature of progress. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 313–328. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Kozlov, D.N.: Chromatic subdivision of a simplicial complex. Homology, Homotopy and Applications 14(1), 1–13 (2012)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Kuznetsov, P.: Understanding non-uniform failure models. Bulletin of the EATCS 106, 53–77 (2012)Google Scholar
  23. 23.
    Kuznetsov, P.: Universal model simulation: BG and extended BG as examples. In: Higashino, T., Katayama, Y., Masuzawa, T., Potop-Butucaru, M., Yamashita, M. (eds.) SSS 2013. LNCS, vol. 8255, pp. 17–31. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  24. 24.
    Linial, N.: Doing the IIS (2010) (unpublished manuscript)Google Scholar
  25. 25.
    Rajsbaum, S.: Iterated shared memory models. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 407–416. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    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)CrossRefGoogle Scholar
  28. 28.
    Raynal, M., Stainer, J.: Synchrony weakened by message adversaries vs asynchrony restricted by failure detectors. In: PODC (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Zohir Bouzid
    • 1
  • Eli Gafni
    • 2
  • Petr Kuznetsov
    • 1
  1. 1.Télécom ParisTechFrance
  2. 2.UCLAUSA

Personalised recommendations