Skip to main content

Asynchronous Computability Theorems for t-Resilient Systems

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Borowsky, E., Gafni, E.: Immediate atomic snapshots and fast renaming, August 1993

    Google Scholar 

  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. 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 1997

    Google Scholar 

  4. Borowsky, E., Gafni, E., Lynch, N.A., Rajsbaum, S.: The BG distributed simulation algorithm. Distrib. Comput. 14(3), 127–146 (2001)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  6. Fischer, M., Lynch, N.A., Paterson, M.S.: Impossibility of distributed commit with one faulty process. J. ACM 32(2), 374–382 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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 2014

    Google Scholar 

  10. Glaser, L.C.: Geometrical Combinatorial Topology, vol. 1. Van Nostrand Reinhold, New York (1970)

    MATH  Google Scholar 

  11. Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  12. Herlihy, M., Kozlov, D., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Elsevier, Boston (2013)

    MATH  Google Scholar 

  13. Herlihy, M., Rajsbaum, S.: The topology of distributed adversaries. Distrib. Comput. 26(3), 173–192 (2013)

    Article  MATH  Google Scholar 

  14. Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  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 1993

    Google Scholar 

  16. Kozlov, D.: Combinatorial Algebraic Topology. Springer, Heidelberg (2008)

    Book  MATH  Google Scholar 

  17. Kozlov, D.N.: Chromatic subdivision of a simplicial complex. Homology, Homotopy Appl. 1(14), 1–13 (2012)

    MathSciNet  MATH  Google Scholar 

  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. Munkres, J.R.: Elements of Algebraic Topology. Addison Wesley, Reading (1984)

    MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vikram Saraph .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Saraph, V., Herlihy, M., Gafni, E. (2016). Asynchronous Computability Theorems for t-Resilient Systems. In: Gavoille, C., Ilcinkas, D. (eds) Distributed Computing. DISC 2016. Lecture Notes in Computer Science(), vol 9888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53426-7_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53426-7_31

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53425-0

  • Online ISBN: 978-3-662-53426-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics