Distributed Computing

, Volume 18, Issue 2, pp 99–109 | Cite as

Tight bounds for shared memory systems accessed by Byzantine processes

  • Noga AlonEmail author
  • Michael Merritt
  • Omer Reingold
  • Gadi Taubenfeld
  • Rebecca N. Wright
Regular Paper


We provide efficient constructions and tight bounds for shared memory systems accessed by n processes, up to t of which may exhibit Byzantine failures, in a model previously explored by Malkhi et al. [21]. We show that sticky bits are universal in the Byzantine failure model for n ≥ 3t + 1, an improvement over the previous result requiring n ≥ (2t + 1)(t + 1). Our result follows from a new strong consensus construction that uses sticky bits and tolerates t Byzantine failures among n processes for any n ≥ 3t + 1, the best possible bound on n for strong consensus. We also present tight bounds on the efficiency of implementations of strong consensus objects from sticky bits and similar primitive objects.


Keywords Shared memory Byzantine agreement Distributed consensus Sticky bits 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Afek, Y., Greenberg, D., Merritt, M., Taubenfeld, G.: Computing with faulty shared memory. J. ACM 42(6), 1231–1274 (1995)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Alon, N., Spencer, J: The Probabilistic Method, Second Edition. Wiley, New York (2000)Google Scholar
  3. 3.
    Attie, P.C.: Wait-free Byzantine Agreement. Technical Report NU-CCS-00-02, College of Computer Science, Northeastern University (2000)Google Scholar
  4. 4.
    Boehm, H.-J.: An almost non-blocking stack. In: Proceedings of the 23rd ACM Symposium on Principles of Distributed Computing, pp. 40–49 (2004)Google Scholar
  5. 5.
    Castro, M., Liskov, B.: Practical Byzantine fault tolerance. In: Proceedings of the 3rd Symposium on Operating Systems Design and Implementation (OSDI'99). New Orleans, LA (1999)Google Scholar
  6. 6.
    Berman, P., Garay, J.A.: Asymptotical optimal distributed consensus. In: Proceedings of the 16th International Colloquium on Automata, Languages and Programming (ICALP 89). LNCS 372, pp. 80–94 (1989)Google Scholar
  7. 7.
    Doherty, S., Herlihy, M., Luchangco, V., Moir, M.: Bringing practical lock-free synchronization to 64-bit applications. In: Proceedings of the 23rd ACM Symposium on Principles of Distributed Computing, pp. 31–39 (2004)Google Scholar
  8. 8.
    Dwork, C., Herlihy, M., Waarts, O.: Contention in shared memory algorithms. J. ACM 44(6), 779–805 (1997)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Fich, F., Herlihy, M., Shavit, N.: On the space complexity of randomized synchronization. J. ACM 45(5), 843–862 (1998)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Füredi, Z.: Tur´n type problems. Surveys in combinatorics, 1991 (Guildford, 1991), 253–300, London Math. Soc. Lecture Note Series. 166, Cambridge University Press, Cambridge (1991)Google Scholar
  12. 12.
    Grötschel, M., Graham, R.L., Lovász, L.: Handbook of Combinatorics, vol. 2. Chap. 24. MIT Press, Cambridge, MA (1995)Google Scholar
  13. 13.
    Herlihy, M.P., Wing, J.M.: Linearizability: a correctness condition for concurrent objects. ACM Trans. Program. Lang. Syst. 12(3), 463–492 (1990)CrossRefGoogle Scholar
  14. 14.
    Herlihy, M.P.: Wait-free synchronization. ACM Trans. Program. Lang. Syst. 13(1), 124–149 (a preliminary version appeared in PODC'88) (1991)CrossRefGoogle Scholar
  15. 15.
    Jayanti, P., Chandra, T., Toueg, S.: Fault-tolerant wait-free shared objects. J. ACM 45(3), 451–500 (1998)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Jayanti, P., Toueg, S.: Some results on the impossibility, universality, and decidability of consensus. In: Proceedings of the 6th International Workshop on Distributed Algorithms LNCS 647, pp. 69–84 (1992)Google Scholar
  17. 17.
    Kihlstrom, K.P., Moser, L.E., Melliar-Smith, P.M.: The SecureRing protocols for securing group communication. In: Proceedings of the 31st IEEE Hawaii International Conference on System Sciences, pp. 317–326 (1998)Google Scholar
  18. 18.
    Ladan-Mozes, E., Shavit, N.: An optimistic approach to lock-free FIFO queues. In: Proceedings of the 18th International Symposium on Distributed Computing. LNCS 3274, pp. 117–131 (2004)Google Scholar
  19. 19.
    Lea, D.: The Java concurrency package JSR-166.
  20. 20.
    Loui, M.C., Abu-Amara, H.: Memory requirements for agreement among unreliable asynchronous processes. Adv. Comput. Res. 4, 163–183 (1987)MathSciNetGoogle Scholar
  21. 21.
    Malkhi, D., Merritt, M., Reiter, M., Taubenfeld, G.: Objects shared by Byzantine processes. Distrib. Comput. 16(1), 37–48 (2003). A preliminary version appeared in Proceedings of the 14th International Symposium on Distributed Computing (DISC 2000). LNCS 1914, pp. 345–359 (2000)CrossRefGoogle Scholar
  22. 22.
    Malkhi, D., Reiter, M.K.: An architecture for survivable coordination in large distributed systems. In: IEEE Transactions on Knowledge and Data Engineering 12(2), 187–202 (2000)CrossRefGoogle Scholar
  23. 23.
    Merritt, M., Reingold, O., Taubenfeld, G., Wright, R.N.: In: Proceedings of the 16th International Symposium on Distributed Computing (DISC 2002). LNCS 2508, pp. 222–236 (2002)Google Scholar
  24. 24.
    Michael, M.M.: Practical lock-free and wait-free LL/SC/VL implementations using 64-Bit CAS. In: 18th International Symposium on Distributed Computing, LNCS 3274, pp. 144–158 (2004)Google Scholar
  25. 25.
    Misra, J.: A simple proof of a simple consensus algorithm. Inform. Process. Lett. 33(1), 21–24 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Pittelli, F.M., Garcia-Molina, H.: Reliable scheduling in a TMR database system. ACM Trans. Comput. Syst. 7(1), 25–60 (1989)CrossRefGoogle Scholar
  27. 27.
    Plotkin, S.A.: Sticky bits and universality of consensus. In: Proceedings of the 8th ACM Symposium on Principles of Distributed Computing, pp. 159–175 (1989)Google Scholar
  28. 28.
    Reiter, M.K.: Distributing trust with the Rampart toolkit. Commun. ACM 39(4), 71–74 (1996)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Shrivastava, S.K., Ezhilchelvan, P.D., Speirs, N.A., Tao, S., Tully, A.: Principal features of the VOLTAN family of reliable node architectures for distributed systems. IEEE Trans. Comput. 41(5), 542–549 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Noga Alon
    • 1
    Email author
  • Michael Merritt
    • 1
  • Omer Reingold
    • 1
  • Gadi Taubenfeld
    • 1
  • Rebecca N. Wright
    • 1
  1. 1.Schools of Mathematics and Computer ScienceTel Aviv UniversityIsrael

Personalised recommendations