Read-Write Memory and k-Set Consensus as an Affine Task

Authors Eli Gafni, Yuan He, Petr Kuznetsov, Thibault Rieutord

Thumbnail PDF


  • Filesize: 0.61 MB
  • 17 pages

Document Identifiers

Author Details

Eli Gafni
Yuan He
Petr Kuznetsov
Thibault Rieutord

Cite AsGet BibTex

Eli Gafni, Yuan He, Petr Kuznetsov, and Thibault Rieutord. Read-Write Memory and k-Set Consensus as an Affine Task. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


The wait-free read-write memory model has been characterized as an iterated Immediate Snapshot (IS) task. The IS task is affine — it can be defined as a (sub)set of simplices of the standard chromatic subdivision. In this paper, we highlight the phenomenon of a "natural" model that can be captured by an iterated affine task and, thus, by a subset of runs of the iterated immediate snapshot model. We show that the read-write memory model in which, additionally, k-set-consensus objects can be used is "natural" by presenting the corresponding simple affine task captured by a subset of 2-round IS runs. As an "unnatural" example, the model using the abstraction of Weak Symmetry Breaking (WSB) cannot be captured by a set of IS runs and, thus, cannot be represented as an affine task. Our results imply the first combinatorial characterization of models equipped with abstractions other than read-write memory that applies to generic tasks.
  • iterated affine tasks
  • k-set consensus
  • k-concurrency
  • simplicial complexes
  • immediate snapshot


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Yehuda Afek, Hagit Attiya, Danny Dolev, Eli Gafni, Michael Merritt, and Nir Shavit. Atomic snapshots of shared memory. Journal of the ACM, 40(4):873-890, 1993. Google Scholar
  2. Yehuda Afek, Eli Gafni, Sergio Rajsbaum, Michel Raynal, and Corentin Travers. The k-simultaneous consensus problem. Distributed Computing, 22(3):185-195, 2010. Google Scholar
  3. Elizabeth Borowsky and Eli Gafni. Generalized FLP impossibility result for t-resilient asynchronous computations. In STOC, pages 91-100, 1993. Google Scholar
  4. Elizabeth Borowsky and Eli Gafni. Immediate atomic snapshots and fast renaming. In PODC, pages 41-51, 1993. Google Scholar
  5. Elizabeth Borowsky and Eli Gafni. A simple algorithmically reasoned characterization of wait-free computation (extended abstract). In PODC, pages 189-198, 1997. Google Scholar
  6. Elizabeth Borowsky, Eli Gafni, Nancy A. Lynch, and Sergio Rajsbaum. The BG distributed simulation algorithm. Distributed Computing, 14(3):127-146, 2001. Google Scholar
  7. Zohir Bouzid, Eli Gafni, and Petr Kuznetsov. Strong equivalence relations for iterated models. In OPODIS, pages 139-154, 2014. Google Scholar
  8. Carole Delporte, Hugues Fauconnier, Sergio Rajsbaum, and Michel Raynal. t-resilient immediate snapshot is impossible. In SIROCCO, pages 177-191, 2016. Google Scholar
  9. Pierre Fraigniaud, Eli Gafni, Sergio Rajsbaum, and Matthieu Roy. Automatically adjusting concurrency to the level of synchrony. In DISC, pages 1-15, 2014. Google Scholar
  10. Eli Gafni. On the wait-free power of iterated-immediate-snapshots. Unpublished manuscript,, 1998.
  11. Eli Gafni. Round-by-round fault detectors (extended abstract): Unifying synchrony and asynchrony. In PODC, 1998. Google Scholar
  12. Eli Gafni. The extended BG-simulation and the characterization of t-resiliency. In STOC, pages 85-92, 2009. Google Scholar
  13. Eli Gafni and Rachid Guerraoui. Simulating few by many: Limited concurrency = set consensus. Unpublished manuscript,, 2009.
  14. Eli Gafni and Rachid Guerraoui. Generalized universality. In CONCUR, pages 17-27, 2011. Google Scholar
  15. Eli Gafni, Yuan He, Petr Kuznetsov, and Thibault Rieutord. Read-write memory and k-set consensus as an affine task. arXiv preprint arXiv:1610.01423, 2016. Google Scholar
  16. Eli Gafni and Petr Kuznetsov. Relating l-resilience and wait-freedom via hitting sets. In ICDCN, pages 191-202, 2011. Google Scholar
  17. Eli Gafni, Petr Kuznetsov, and Ciprian Manolescu. A generalized asynchronous computability theorem. In PODC, pages 222-231, 2014. Google Scholar
  18. Eli Gafni and Sergio Rajsbaum. Distributed programming with tasks. In OPODIS, pages 205-218, 2010. Google Scholar
  19. Eli Gafni, Sergio Rajsbaum, and Maurice Herlihy. Subconsensus tasks: Renaming is weaker than set agreement. In DISC, pages 329-338, 2006. Google Scholar
  20. Eli Gafni, Michel Raynal, and Corentin Travers. Test & set, adaptive renaming and set agreement: A guided visit to asynchronous computability. In SRDS, pages 93-102, 2007. Google Scholar
  21. Maurice Herlihy. Wait-free synchronization. ACM Transactions on Programming Languages and Systems, 13(1):123-149, January 1991. Google Scholar
  22. Maurice Herlihy, Dmitry N. Kozlov, and Sergio Rajsbaum. Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, 2014. Google Scholar
  23. Maurice Herlihy and Sergio Rajsbaum. The topology of shared-memory adversaries. In PODC, pages 105-113, 2010. Google Scholar
  24. Maurice Herlihy and Nir Shavit. The topological structure of asynchronous computability. Journal of the ACM, 46(2):858-923, 1999. Google Scholar
  25. Damien Imbs, Sergio Rajsbaum, and Adrián Valle. Untangling partial agreement: Iterated x-consensus simulations. In SSS, pages 139-155, 2015. Google Scholar
  26. Dmitry N. Kozlov. Chromatic subdivision of a simplicial complex. Homology, Homotopy and Applications, 14(2):197-209, 2012. Google Scholar
  27. Achour Mostéfaoui, Michel Raynal, and Corentin Travers. Exploring gafni’s reduction land: From Omega^k to wait-free adaptive (2p-[p/k])-renaming via k-set agreement. In DISC, pages 1-15, 2006. Google Scholar
  28. Sergio Rajsbaum, Michel Raynal, and Corentin Travers. The iterated restricted immediate snapshot model. In COCOON, pages 487-497, 2008. Google Scholar
  29. Michel Raynal and Julien Stainer. Increasing the power of the iterated immediate snapshot model with failure detectors. In SIROCCO, pages 231-242, 2012. Google Scholar
  30. Michel Raynal, Julien Stainer, and Gadi Taubenfeld. Distributed universality. In OPODIS, pages 469-484, 2014. Google Scholar
  31. Michael Saks and Fotios Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM J. on Computing, 29:1449-1483, 2000. Google Scholar
  32. Vikram Saraph, Maurice Herlihy, and Eli Gafni. Asynchronous computability theorems for t-resilient systems. In DISC, pages 428-441, 2016. Google Scholar
  33. Edwin H. Spanier. Algebraic topology. McGraw-Hill Book Co., New York, 1966. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail