Asynchronous Computability Theorems for t-Resilient Systems

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9888)

Abstract

A task is a distributed coordination problem where processes start with private inputs, communicate with one another, and then halt with private outputs. A protocol that solves a task is t-resilient if it tolerates halting failures by t or fewer processes. The t-resilient asynchronous computability theorem stated here characterizes the tasks that have t-resilient protocols in a shared-memory model. This result generalizes the prior (wait-free) asynchronous computability theorem of Herlihy and Shavit to a broader class of failure models, and requires introducing several novel concepts.

References

  1. 1.
    Borowsky, E., Gafni, E.: Immediate atomic snapshots and fast renaming, August 1993Google Scholar
  2. 2.
    Borowsky, E.: Capturing the power of resiliency and set consensus in distributed systems. Ph.D. thesis, University of California, Los Angeles (1995)Google Scholar
  3. 3.
    Borowsky, E., Gafni, E.: A simple algorithmically reasoned characterization of wait-free computations. In: Proceedings of the 16th Annual ACM Symposium on Principles of Distributed Computing, pp. 189–198, August 1997Google Scholar
  4. 4.
    Borowsky, E., Gafni, E., Lynch, N.A., Rajsbaum, S.: The BG distributed simulation algorithm. Distrib. Comput. 14(3), 127–146 (2001)CrossRefGoogle Scholar
  5. 5.
    Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Tielmann, A.: The disagreement power of an adversary. In: Keidar, I. (ed.) DISC 2009. LNCS, vol. 5805, pp. 8–21. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Fischer, M., Lynch, N.A., Paterson, M.S.: Impossibility of distributed commit with one faulty process. J. ACM 32(2), 374–382 (1985)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Gafni, E., Kuznetsov, P.: On l-resilience, hitting sets, and colorless tasks. In: Proceedings of the 29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2010, pp. 81–82. ACM, New York (2010)Google Scholar
  8. 8.
    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
  9. 9.
    Gafni, E., Kuznetsov, P., Manolescu, C.: A generalized asynchronous computability theorem. In: ACM Symposium on Principles of Distributed Computing, PODC 2014, Paris, France, pp. 222–231, 15–18 July 2014Google Scholar
  10. 10.
    Glaser, L.C.: Geometrical Combinatorial Topology, vol. 1. Van Nostrand Reinhold, New York (1970)MATHGoogle Scholar
  11. 11.
    Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)MATHGoogle Scholar
  12. 12.
    Herlihy, M., Kozlov, D., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Elsevier, Boston (2013)MATHGoogle Scholar
  13. 13.
    Herlihy, M., Rajsbaum, S.: The topology of distributed adversaries. Distrib. Comput. 26(3), 173–192 (2013)CrossRefMATHGoogle Scholar
  14. 14.
    Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Herlihy, M.P., Shavit, N.: The asynchronous computability theorem for t-resilient tasks. In: Symposium on Theory of Computing (STOC), pp. 111–120. ACM, May 1993Google Scholar
  16. 16.
    Kozlov, D.: Combinatorial Algebraic Topology. Springer, Heidelberg (2008)CrossRefMATHGoogle Scholar
  17. 17.
    Kozlov, D.N.: Chromatic subdivision of a simplicial complex. Homology, Homotopy Appl. 1(14), 1–13 (2012)MathSciNetMATHGoogle Scholar
  18. 18.
    Kozlov, D.N.: Combinatorial topology of the standard chromatic subdivision and weak symmetry breaking for 6 processes. CoRR, abs/1506.03944 (2015)Google Scholar
  19. 19.
    Munkres, J.R.: Elements of Algebraic Topology. Addison Wesley, Reading (1984)MATHGoogle Scholar
  20. 20.
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA
  2. 2.Department of Computer ScienceUCLALos AngelesUSA

Personalised recommendations