Mathematical systems theory

, Volume 26, Issue 1, pp 3–19 | Cite as

Cloture Votes:n/4-resilient Distributed Consensus int + 1 rounds

  • Piotr Berman
  • Juan A. Garay


TheDistributed Consensus problem involvesn processors each of which holds an initial binary value. At mostt processors may be faulty and ignore any protocol (even behaving maliciously), yet it is required that the nonfaulty processors eventually agree on a value that was initially held by one of them. We measure the quality of a consensus protocol using the following parameters; total number of processorsn, number of rounds of message exchanger, and maximal message sizem. The known lower bounds are respectively 3t + 1,t + 1, and 1.

While no known protocol is optimal in all these three aspects simultaneously,Cloture Votes—the protocol presented in this paper—takes further steps in this direction, by making consensus possible withn = 4t + 1,r = t + 1, and polynomial message size.

Cloture is a parliamentary procedure (also known as “parliamentary guillotine”) which makes it possible to curtail unnecessary long debates. In our protocol the unanimous will of the correct processors (akin to parliamentarian supermajority) may curtail the debate. This is facilitated by having the processors open in each round a new process (debate), which either ends quickly, with the conclusion “continue” or “terminate with the default value,” or lasts through many rounds. Importantly, in the latter case the messages being sent are short.


Message Size Consensus Protocol 16th International Colloquium Byzantine Agreement Faulty Processor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BD]
    A. Bar-Noy and D. Dolev, Families of Consensus Algorithms,Proc. 3rd Aegean Workshop on Computing, pp. 380–390, June/July 1988.Google Scholar
  2. [BDDS]
    A. Bar-Noy, D. Dolev, C. Dwork, and H. R. Strong, Shifting Gears: Changing Algorithms on the Fly To Expedite Byzantine Agreement,Proc. 6th Annual ACM Symp. on Principles of Distributed Computing, pp. 42–51, August 1987.Google Scholar
  3. [BG1]
    P. Berman and J. A. Gray, Asymptotically Optimal Distributed Consensus,Proc. 16th International Colloquium on Automata, Languages and Programming, pp. 80–94, LNCS, Vol. 372, July 1989.Google Scholar
  4. [BG2]
    P. Berman and J. A. Garay, Efficient Distributed Consensus withn = (3 + ɛ)t Processors,Proc. 5th International Workshop on Distributed Algorithms, pp. 129–142, LNCS 579, October 1991.Google Scholar
  5. [BGP]
    P. Berman, J. A. Garay, and K. J. Perry, Towards Optimal Distributed Consensus,Proc. 30th IEEE Symp. on Foundations of Computer Science, pp. 410–415, October/November 1989.Google Scholar
  6. [BL]
    J. Burns and N. Lynch, The Byzantine Firing Squad Problem,Advances in Computing Research, Vol. 4 (1987), pp. 147–161.MathSciNetGoogle Scholar
  7. [C1]
    B. Coan, A Communication-Efficient Canonical Form for Fault-Tolerant Distributed Protocols,Proc. 5th Annual ACM Symp. on Principles of Distributed Computing, pp. 63–72, August 1986.Google Scholar
  8. [C2]
    B. Coan, Efficient Agreement Using Fault Diagnosis,Proc. 26th Allerton Conf. on Communication, Control and Computing, pp. 663–672, 1988.Google Scholar
  9. [CW1]
    B. Coan and J. Welch, Modular Construction of Nearly Optimal Byzantine Agreement Protocols,Proc. 9th Annual ACM Symp. on Principles of Distributed Computing, pp. 295–306, August 1989.Google Scholar
  10. [CW2]
    B. Coan and J. Welch, Modular Construction of an Efficient 1-Bit Byzantine Agreement Protocol,Mathematical Systems Theory, this issue, pp. 131–154.Google Scholar
  11. [DRS]
    D. Dolev, R. Reischuk, and H. R. Strong, Early Stopping in Byzantine Agreement,Journal of the ACM, Vol. 37, No. 4 (1990), pp. 720–741.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [DS]
    D. Dolev and H. R. Strong, Polynomial Algorithms for Multiple Processor Agreement,Proc. 14th Annual ACM Symp. on Theory of Computing, pp. 401–407, May 1982.Google Scholar
  13. [FM]
    P. Feldman and S. Micali, An Optimal Probabilistic Algorithm for Byzantine Agreement (invited paper),Proc. 16th International Colloquium on Automata, Languages and Programming, LNCS, Vol. 372, pp. 341–378, July 1989.MathSciNetCrossRefGoogle Scholar
  14. [FL]
    M. J. Fischer and N. Lynch, A Lower Bound for the Time to Assure Interactive Consistency,Information Processing Letters, Vol. 14, No. 4 (1982), pp. 183–186.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [HM]
    J. Halpern and Y. Moses, Knowledge and Common Knowledge in a Distributed Environment,Journal of the ACM, Vol. 37, No. 3 (1990), pp. 549–587.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [LSP]
    L. Lamport, R. E. Shostak, and M. Pease, The Byzantine Generals Problem,ACM Transactions on Programming Languages and Systems, Vol. 4, No. 3 (1982), pp. 382–401.zbMATHCrossRefGoogle Scholar
  17. [MW]
    Y. Moses and O. Waarts, Coordinated Traversal: (t + 1)-Round Byzantine Agreement in Polynomial Time,Proc. 29th IEEE Symp. on Foundations of Computer Science, pp. 246–255, October 1988.Google Scholar
  18. [PSL]
    M. Pease, R. Shostak, and L. Lamport, Reaching Agreement in the Presence of Faults,Journal of the ACM, Vol. 27, No. 2 (1980), pp. 228–234.MathSciNetzbMATHCrossRefGoogle Scholar
  19. [TPS]
    S. Toueg, K. J. Perry, and T. K. Srikanth, Fast Distributed Agreement,SIAM Journal on Computing, Vol. 16, No. 3 (1987), pp. 445–458.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • Piotr Berman
    • 1
  • Juan A. Garay
    • 2
  1. 1.Department of Computer ScienceThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.IBM T. J. Watson Research CenterYorktown HeightsUSA

Personalised recommendations