Mathematical systems theory

, Volume 28, Issue 5, pp 421–435 | Cite as

Unison, canon, and sluggish clocks in networks controlled by a synchronizer

  • S. Even
  • S. Rajsbaum


The effect of using a simple synchronizer on the performance of a directed, strongly connected, distributed network, is analysed. In this paper we assume that the time of message transmission is positive but negligible. It is shown that the synchronizer is sufficient to assure that a full rate of computation is achieved in networks with a global clock, in spite of the absence of a global start-up signal. In fact,unison is reached within linear time. A similar phenomenon occurs if there is no global clock, but all local clocks have the same rate. In case the local clocks do not have the same rate, it is shown that the computational rate is not slower than anysluggish clock; i.e., a clock such that between any two of its ticks, every local clock ticks at least once.


Computational Mathematic Linear Time Message Transmission Full Rate Local Clock 
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. [1]
    B. Awerbuch, Complexity of network synchronization,Journal of the Association for Computing Machinery, Vol. 32, No. 4, Oct. 1985, pp. 804–823.Google Scholar
  2. [2]
    A. Arora, S. Dolev, and M. Gouda, Maintaining digital clocks in step,Parallel Processing Letters, Vol. 1, No. 1, Sept. 1991, pp. 11–18.Google Scholar
  3. [3]
    K. M. Chandy and L. Lamport, Distributed snapshots: Determining global states of distributed systems,ACM Transactions on Computer Systems, Vol. 3, No. 1, Feb. 1985, pp. 63–75.Google Scholar
  4. [4]
    F. Commoner, A. W. Holt, S. Even, and A. Pnueli, Marked Directed Graphs,Journal of Computer and System Sciences, Vol. 5, No. 5, Oct. 1971, pp. 511–523.Google Scholar
  5. [5]
    E. W. Dijkstra, Self-stabilizing systems in spite of distributed control,Communications of the ACM, Vol. 17, No. 11, 1974, pp. 643–644.Google Scholar
  6. [6]
    S. Even, and S. Rajsbaum, Unison in distributed networks, inSequences, Combinatorics, Compression, Security and Transmission, R. M. Capocelli (ed.), Springer-Verlag, New York, 1990, pp. 479–487.Google Scholar
  7. [7]
    S. Even, and S. Rajsbaum, The use of a synchronizer yields maximum computation rate in distributed networks,Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, 1990, pp. 95–105. To appear inMathematical Systems Theory.Google Scholar
  8. [8]
    R. G. Gallager, Distributed Minimum Hop Algorithms, Technical Report LIDS-P-1175, M.I.T., Cambridge, MA, Jan. 1982.Google Scholar
  9. [9]
    H. J. Genrich, Einfache Nicht-Sequentielle Prozesse, Gesellschaft für Mathematik und Datenverarbeitung, Birlinghoven, Germany, 1970.Google Scholar
  10. [10]
    M. G. Gouda, and T. Herman, Stabilizing unison,Information Processing Letters, Vol. 35, No. 4, 1990, pp. 171–175.Google Scholar
  11. [11]
    T. Jiang, The Synchronization of Nonuniform Networks of Finite Automata, Technical Report 89-03, McMaster University, Ontario, 1989. Also inProceedings of the 30th Annual Symposium on Foundations of Computer Science, 1989, pp. 376–381.Google Scholar
  12. [12]
    E. F. Moore, The firing squad synchronization problem, inSequential Machines, Selected Papers, Addison-Wesley, Reading, MA, 1964, pp. 213–214.Google Scholar
  13. [13]
    P. Rosenstiehl, J. R. Fiksel, and A. Holliger, Intelligent graphs: Networks of finite automata capable of solving graph problems, inGraph Theory and Computing, R. C. Read (ed.), Academic Press, New York, 1972, pp. 219–265.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1995

Authors and Affiliations

  • S. Even
    • 1
  • S. Rajsbaum
    • 2
  1. 1.Department of Computer Science, TechnionHaifaIsrael
  2. 2.Instituto de MatemáticasU.N.A.M.D.F. 04510, Mexico

Personalised recommendations