Advertisement

Synchronization of 1-way connected processors

  • Salvatore La Torre
  • Margherita Napoli
  • Mimmo Parente
Technical Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1279)

Abstract

We are given a network of n identical processors that work synchronously at discrete steps. At each time step every processor sends messages only to a given subset of its neighbouring processors and receives only from the remaining neighbours. The computation starts with one distinguished processor in a particular starting state and all other processors in a quiescent state. The problem is the following: to set all the processors in a given state for the first time and at the very same instant. This problem is known as the Firing Squad Synchronization Problem and was introduced by Moore in 1964. The usual formulation is given on cellular automata and it has been investigated on various topologies of networks of processors and for various kinds of communication. In this paper we present for the first time solutions that synchronize processors that communicate on 1-way links and are arranged in a ring or in a square whose rows and columns are rings. In particular we provide algorithms to synchronize both the two networks and prove that all such algorithms are optimal in time. In addition we show how to compose solutions to obtain new synchronizing solutions. In particular given two solutions in time t1(n) and t2 (n) we provide solutions in time t1(n)+t2(n)+d and t1(n)t2(n). Moreover, given a predicate P(n), a solution is given whose time is t1(n), if P(n) holds, and t2(n) otherwise. Finally, we give solutions which synchronize at a given time f(n), for f(n) equal to n2, n log n and 2n.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Balzer, An 8-states minimal time solution to the firing squad synchronization problem. Information and Control 10 (1967), 22–42.CrossRefGoogle Scholar
  2. 2.
    K. Culik, Variations of the firing squad problem and applications. Information Processing Letters, 30 (1989), 153–157.CrossRefGoogle Scholar
  3. 3.
    K. Kobayashy, The Firing Squad Synchronization Problem for Two-Dimensional Arrays. Information and Control 34 (1977), 177–197.CrossRefGoogle Scholar
  4. 4.
    S. La Torre, M. Napoli and M. Parente, Synchronization of a line of identical processors at a given time. Proc. of TAPSOFT'97, L.N.C.S. 1214 (1997), 405–416.Google Scholar
  5. 5.
    J. Mazoyer, A six states minimal time solution to the firing squad synchronization problem. Theoretical Computer Science 50 (1987), 183–238.Google Scholar
  6. 6.
    J.Mazoyer and N.Reimen, A linear speed-up theorem for cellular automata. Theoretical Computer Science 101 (1992), 59–98.Google Scholar
  7. 7.
    J. Mazoyer, A Minimal Time Solution to the Firing Squad Synchronization Problem with only one bit of Information Exchanged. To appear on Theoretical Computer Science.Google Scholar
  8. 8.
    F. Minsky, Computation: Finite and Infinite Machines. Prentice-Hall, 1967.Google Scholar
  9. 9.
    E. F. Moore, Sequential Machines, Selected Papers. Addison-Wesley, Reading, Mass, 1964.Google Scholar
  10. 10.
    I. Shinahr, Two-and Three-Dimensional Firing-Squad Synchronization Problems. Information and Control 24 (1974), 163–180.CrossRefGoogle Scholar
  11. 11.
    A. Waksman, An optimum solution to the firing squad synchronization problem. Information and Control 9 (1966), 66–78.CrossRefGoogle Scholar
  12. 12.
    www.unisa.it/papers/fct.ps.gzGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Salvatore La Torre
    • 1
  • Margherita Napoli
    • 1
  • Mimmo Parente
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversità degli Studi di SalernoBaronissiItaly

Personalised recommendations