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Resilient Consensus for Infinitely Many Processes

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Book cover Distributed Computing (DISC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2848))

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Abstract

We provide results for implementing resilient consensus for a (countably) infinite collection of processes.

  • For a known number of faults, we prove the following equivalence result: For every t≥ 1, there is a t-resilient consensus object for infinitely many processes if and only if there is a t-resilient consensus object for t+1 processes.

  • For an unknown or infinite number of faults, we consider whether an infinite set of wait-free consensus objects, capable of solving consensus for any finite collection of processes, suffice to solve wait-free consensus for infinitely many processes. We show that this implication holds under an assumption precluding runs in which the number of simultaneously active processes is not bounded, leaving the general question open.

All the proofs are constructive and several of the constructions have adaptive time complexity. (Reduced to the finite domain, some improve on the time complexity of known results.) Furthermore, we prove that the constructions are optimal in some space parameters by providing tight simultaneous-access and space lower bounds. Finally, using known techniques, we draw new conclusions on the universality of resilient consensus objects in the infinite domain.

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References

  1. Aspnes, J., Shah, G., Shah, J.: Wait-free consensus with infinite arrivals. In: Proc. 34th Annual Syrup. on Theory of Computing, May 2002, pp. 524–533 (2002)

    Google Scholar 

  2. Attiya, H., Bortnikov, V.: Adaptive and efficient mutual exclusion. In: Proc. 19th ACM Symp. on Principles of Distributed Computing, July 2000, pp. 91–100 (2000)

    Google Scholar 

  3. Borowsky, E., Gafni, E., Afek, Y.: Consensus power makes (some) sense! In: Proc. 13th ACM Syrup. on Principles of Distributed Computing, August 1994, pp. 363–372 (1994)

    Google Scholar 

  4. Chandra, T., Hadzilacos, V., Jayanti, P., Toueg, S.: Wait-freedom vs. t-resiliency and the robustness of wait-free hierarchies. In: Proc. 13th ACM Symp. on Principles of Distributed Computing, August 1994, pp. 334–343 (1994), Expanded version: www.cs.toronto.edu/vassos/research/list-of-publications.html

  5. Chocker, G., Malkhi, D.: Active disk paxos with infinitely many processes. In: Proc. 21th ACM Symp. on Principles of Distributed Computing, July 2002, pp. 78–87 (2002)

    Google Scholar 

  6. Fich, F., Herlihy, M., Shavit, N.: On the Space Complexity of Randomized Synchronization. Journal of the ACM 45(5), 843–862 (1998)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Gafni, E., Merritt, M., Taubenfeld, G.: The concurrency hierarchy, and algorithms for unbounded concurrency. In: Proc. 20th ACM Symp. on Principles of Distributed Computing, August 2001, pp. 161–169 (2001)

    Google Scholar 

  9. Herlihy, M.P., Wing, J.M.: Linearizability: A correctness condition for concurrent objects. ACM Transactions on Programming Languages and Systems 12(3), 463–492 (1990)

    Article  Google Scholar 

  10. Herlihy, M.P.: Wait-free synchronization. ACM Transactions on Programming Languages and Systems 13(1), 124–149 (1991)

    Article  Google Scholar 

  11. Jayanti, P., Toueg, S.: Some results on the impossibility, universality and decidability of consensus. In: Segall, A., Zaks, S. (eds.) WDAG 1992. LNCS, vol. 647, pp. 69–84. Springer, Heidelberg (1992)

    Google Scholar 

  12. Lo, W.K., Hadzilacos, V.: On the power of shared objects to implement one-resilient consensus. Distributed Computing 13(4), 219–238 (2000)

    Article  Google Scholar 

  13. Loui, M.C., Abu-Amara, H.: Memory requirements for agreement among unreliable asynchronous processes. Advances in Computing Research 4, 163–183 (1987)

    MathSciNet  Google Scholar 

  14. Malkhi, D., Merritt, M., Reiter, M., Taubenfeld, G.: Objects shared by Byzantine processes. Distributed Computing 16(1), 37–48 (2003); Also in Herlihy, M.P. (ed.): DISC 2000. LNCS, vol. 1914, pp. 345–359. Springer, Heidelberg (2000)

    Book  MATH  Google Scholar 

  15. Merritt, M., Taubenfeld, G.: Speeding Lamport’s fast mutual exclusion algorithm. Information Processing Letters 45, 137–142 (1991); Also published as an AT&T technical memorandum (May 1991)

    Article  Google Scholar 

  16. Merritt, M., Taubenfeld, G.: Computing with ininitely many processes. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, pp. 164–178. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  17. Plotkin, S.A.: Sticky bits and universality of consensus. In: Proc. 8th ACM Symp. on Principles of Distributed Computing, August 1989, pp. 159–175 (1989)

    Google Scholar 

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Author information

Authors and Affiliations

  1. AT&T Labs, 180 Park Ave., Florham Park, NJ, 07932, USA

    Michael Merritt

  2. School of computer science, the Interdisciplinary Center, P.O.Box 167, Herzliya, 46150, Israel

    Gadi Taubenfeld

Authors
  1. Michael Merritt
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  2. Gadi Taubenfeld
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Editor information

Editors and Affiliations

  1. University of Toronto,  

    Faith Ellen Fich

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© 2003 Springer-Verlag Berlin Heidelberg

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Merritt, M., Taubenfeld, G. (2003). Resilient Consensus for Infinitely Many Processes. In: Fich, F.E. (eds) Distributed Computing. DISC 2003. Lecture Notes in Computer Science, vol 2848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39989-6_1

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  • DOI: https://doi.org/10.1007/978-3-540-39989-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20184-7

  • Online ISBN: 978-3-540-39989-6

  • eBook Packages: Springer Book Archive

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