Algorithmica

, Volume 3, Issue 1–4, pp 121–169 | Cite as

Programming simultaneous actions using common knowledge

  • Yoram Moses
  • Mark R. Tuttle
Article

Abstract

This work applies the theory of knowledge in distributed systems to the design of efficient fault-tolerant protocols. We define a large class of problems requiring coordinated, simultaneous action in synchronous systems, and give a method of transforming specifications of such problems into protocols that areoptimal in all runs: these protocols are guaranteed to perform the simultaneous actions as soon as any other protocol could possibly perform them, given the input to the system and faulty processor behavior. This transformation is performed in two steps. In the first step we extract, directly from the problem specification, a high-level protocol programmed using explicit tests for common knowledge. In the second step we carefully analyze when facts become common knowledge, thereby providing a method of efficiently implementing these protocols in many variants of the omissions failure model. In the generalized omissions model, however, our analysis shows that testing for common knowledge is NP-hard. Given the close correspondence between common knowledge and simultaneous actions, we are able to show that no optimal protocol for any such problem can be computationally efficient in this model. The analysis in this paper exposes many subtle differences between the failure models, including the precise point at which this gap in complexity occurs.

Key words

Common knowledge Simultaneous action Byzantine agreement Distributed firing squad Omissions failure model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BL]
    J. Burns and N. A. Lynch, The Byzantine firing squad problem, MIT Technical Report MIT/LCS/TM-275, 1985.Google Scholar
  2. [CM]
    K. M. Chandy and J. Misra, How processes learn,Distrib. Comput.,1(1), 1986, 40–52.MATHCrossRefGoogle Scholar
  3. [C]
    B. Coan, A communication-efficient canonical form for fault-tolerant distributed protocols,Proceedings of the Fifth PODC, 1985, pp. 63–72.Google Scholar
  4. [CDDS]
    B. Coan, D. Dolev, C. Dwork, and L. Stockmeyer, The distributed firing squad problem,Proceedings of the Seventeenth STOC, 1985, pp. 335–345.Google Scholar
  5. [DRS]
    D. Dolev, R. Reischuk, and H. R. Strong, Eventual is earlier than immediate,Proceedings of the 23th FOCS, 1982, pp. 196–203.Google Scholar
  6. [DM]
    C. Dwork and Y. Moses, Knowledge and common knowledge in a Byzantine environment: The case of crash failures,Proceedings of the Conference on Theoretical Aspects of Reasoning About Knowledge, Monterey, 1986, J. Y. Halpern ed., Morgan Kaufmann, Los Altos, CA, pp. 149–170. Slightly revised as MITTechnical Report MIT/LCS/TM-300, 1986. To appear inInformation and Computation.Google Scholar
  7. [F]
    M. J. Fisher, The consensus problem in unreliable distributed systems (a brief survey), Yale University Technical Report YALEU/DCS/RR-273, 1983.Google Scholar
  8. [FI]
    M. J. Fischer and N. Immerman, Foundations of knowledge for distributed systems,Proceedings of the Conference on Theoretical Aspects of Reasoning About Knowledge, Monterey, 1986, J. Y. Halpern ed., Morgan Kaufmann, Los Altos, CA, pp. 171–185.Google Scholar
  9. [FL]
    M. J. Fischer and N. A. Lynch, A lower bound for the time to assure interactive consistency,Infor. Process. Lett.,14(4), 1982, 183–186.MATHCrossRefMathSciNetGoogle Scholar
  10. [GJ]
    M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, San Francisco, 1979.MATHGoogle Scholar
  11. [Ha]
    V. Hadzilacos, A lower bound for Byzantine agreement with fail-stop processors, Harvard University Technical Report TR-21-83.Google Scholar
  12. [HF]
    J. Y. Halpern and R. Fagin, A formal model of knowledge, action, and communication in distributed systems,Proceedings of the Fourth PODC, 1985, pp. 224–236.Google Scholar
  13. [HM1]
    J. Y. Halpern and Y. Moses, Knowledge and common knowledge in a distributed environment. Version of August 1987 is available as IBM Research Report RJ 4421. Early versions appeared inProceedings of the Third PODC, 1984, pp. 50–61; and as IBM Research Report RJ 4421, 1984 and 1986.Google Scholar
  14. [HM2]
    J. Y. Halpern and Y. Moses, A guide to the modal logic of knowledge and belief,Proceedings of the Ninth IJCAI, 1985, pp. 480–490.Google Scholar
  15. [Hi]
    J. Hintikka,Knowledge and Belief, Cornell University Press, Ithaca, NY, 1962.Google Scholar
  16. [HU]
    J. E. Hopcroft and J. D. Ullman,Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Massachusetts, 1979.MATHGoogle Scholar
  17. [LF]
    L. Lamport and M. J. Fischer, Byzantine generals and transaction commit protocols, SRI Technical Report Op. 62, 1982.Google Scholar
  18. [Mi]
    R. Michel, Attaining common knowledge in synchronous distributed networks, unpublished manuscript, 1986.Google Scholar
  19. [MSF]
    C. Mohan, H. R. Strong, and S. Finkelstein, Methods for distributed transaction commit and recovery using Byzantine agreement within clusters of processors,Proceedings of the Second PODC, 1983, pp. 89–103.Google Scholar
  20. [Mo]
    Y. Moses, Knowledge in a distributed environment, Ph.D. Thesis, Stanford University Technical Report STAN-CS-1120, 1986.Google Scholar
  21. [PR]
    R. Parikh and R. Ramanujam, Distributed processes and the logic of knowledge (preliminary report),Proceedings of the Workshop on Logics of Programs, 1985, pp. 256–268.Google Scholar
  22. [PSL]
    M. Pease, R. Shostak, and L. Lamport, Reaching agreement in the presence of faults,J. Assoc. Comput. Mach.,27(2), 1980, 228–234.MATHMathSciNetGoogle Scholar
  23. [PT]
    K. Perry and S. Toueg, Distributed agreement in the presence of processor and communication faults,IEEE Trans. Software Engrg,12(3), 1986, 477–482.Google Scholar
  24. [R]
    M. O. Rabin, Efficient solutions to the distributed firing squad problem, private communication.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Yoram Moses
    • 1
  • Mark R. Tuttle
    • 2
  1. 1.Department of Applied MathematicsWeizmann InstituteRehovotIsrael
  2. 2.Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations