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Optimally simulating crash failures in a byzantine environment

  • Rida Bazzi
  • Gil Neiger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 579)

Abstract

The difficulty of designing of fault-tolerant distributed algorithms increases with the severity of failures that an algorithm must tolerate. Researchers have simplified this task by developing methods that automatically translate protocols tolerant of “benign” failures into ones tolerant of more “severe” failures. In addition to simplifying the design task, these translations can provide insight into the relative impact of different models of faulty behavior on the ability to provide fault-tolerant applications. Such insights can be gained by examining the properties of the translations. The roundcomplexity of a translation is such a property; it is the number of rounds of communication that the translation uses to simulate one round of the original algorithm. This paper considers synchronous systems and examines the problem of developing translations from simple stopping (crash) failures to completely arbitrary behavior with round-complexities 2, 3, and 4, respectively. In each case, we show a lower bound on the number of processors that must remain correct. We show matching upper bounds for all of these by developing three new translation techniques that are each optimal in the number of processors required. These results fully characterize the optimal translations between crash and arbitrary failures.

Keywords

Impossibility Result Synchronous System Byzantine Agreement State Transition Function Faulty Behavior 
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.

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References

  1. [1]
    Amotz Bar-Noy, Danny Dolev, Cynthia Dwork, and H. Raymond Strong. Shifting gears: Changing algorithms on the fly to expedite Byzantine agreement (preliminary report). In Proceedings of the Sixth ACM Symposium on Principles of Distributed Computing, pages 42–51, August 1987. Revised version received November 1988.Google Scholar
  2. [2]
    Piotr Berman and Juan A. Garay. Asymptotically optimal consensus. In Proceedings of the Sixteenth International Conference on Automata, Languages, and Programming, volume 372 of Lecture Notes on Computer Science, pages 80–94. Springer-Verlag, 1989.Google Scholar
  3. [3]
    Piotr Berman, Juan A. Garay, and Kenneth J. Perry. Towards optimal distributed consensus. In Proceedings of the Thirtieth Symposium on Foundations of Computer Science, pages 410-415. IEEE Computer Society Press, October 1989.Google Scholar
  4. [4]
    Brian A. Coan. A communication-efficient canonical form for fault-tolerant distributed protocols. In Proceedings of the Fifth ACM Symposium on Principles of Distributed Computing, pages 63–72, August 1986. A revised version appears in Coan's Ph.D. dissertation [5].Google Scholar
  5. [5]
    Brian A. Coan. Achieving Consensus in Fault-Tolerant Distributed Computer Systems: Protocols, Lower Bounds, and Simulations. Ph.D. dissertation, Massachusetts Institute of Technology, June 1987.Google Scholar
  6. [6]
    Brian A. Coan. A compiler that increases the fault-tolerance of asynchronous protocols. IEEE Transactions on Computers, 37(12):1541–1553, December 1988.Google Scholar
  7. [7]
    Danny Dolev. The Byzantine generals strike again. Journal of Algorithms, 3(1):14–30, 1982.Google Scholar
  8. [8]
    Vassos Hadzilacos. Byzantine agreement under restricted types of failures (not telling the truth is different from telling lies). Technical Report 18-83, Department of Computer Science, Harvard University, 1983. A revised version appears in Hadzilacos's Ph.D. dissertation [9].Google Scholar
  9. [9]
    Vassos Hadzilacos. Issues of Fault Tolerance in Concurrent Computations. Ph.D. dissertation, Harvard University, June 1984. Department of Computer Science Technical Report 11–84.Google Scholar
  10. [10]
    Vassos Hadzilacos. Connectivity requirements for Byzantine agreement under restricted types of failures. Distributed Computing, 2(2):95–103, 1987.Google Scholar
  11. [11]
    Joseph Y. Halpern and Yoram Moses. Knowledge and common knowledge in a distributed environment. Journal of the ACM, 37(3):549–587, July 1990.Google Scholar
  12. [12]
    Joseph Y. Halpern and H. Raymond Strong, March 1986. Personal communication.Google Scholar
  13. [13]
    Leslie Lamport, Robert Shostak, and Marshall Pease. The Byzantine generals problem. ACM Transactions on Programming Languages and Systems, 4(3):382–401, July 1982.Google Scholar
  14. [14]
    Yoram Moses and Mark R. Tuttle. Programming simultaneous actions using common knowledge. Algorithmica, 3(1):121–169, 1988.Google Scholar
  15. [15]
    Gil Neiger and Sam Toueg. Automatically increasing the fault-tolerance of distributed algorithms. Journal of Algorithms, 11(3):374–419, September 1990.Google Scholar
  16. [16]
    Gil Neiger and Mark R. Tuttle. Common knowledge and consistent simultaneous coordination. In J. van Leeuwen and N. Santoro, editors, Proceedings of the Fourth International Workshop on Distributed Algorithms, volume 486 of Lecture Notes on Computer Science, pages 334–352. Springer-Verlag, September 1990. To appear in Distributed Computing. Google Scholar
  17. [17]
    Kenneth J. Perry and Sam Toueg. Distributed agreement in the presence of processor and communication faults. IEEE Transactions on Software Engineering, 12(3):477–482, March 1986.Google Scholar
  18. [18]
    Richard D. Schlichting and Fred B. Schneider. Fail-stop processors: an approach to designing fault-tolerant computing systems. ACM Transactions on Computer Systems, 1(3):222–238, August 1983.Google Scholar
  19. [19]
    T. K. Srikanth and Sam Toueg. Simulating authenticated broadcasts to derive simple fault-tolerant algorithms. Distributed Computing, 2(2):80–94, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Rida Bazzi
    • 1
  • Gil Neiger
    • 1
  1. 1.College of ComputingGeorgia Institute of TechnologyAtlantaUSA

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