Skip to main content
SpringerLink
Log in

Optimal Time and Communication Solutions of Firing Squad Synchronization Problems on Square Arrays, Toruses and Rings

  • Conference paper
Book cover Developments in Language Theory (DLT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3340))

Included in the following conference series:

Abstract

A new solution for the Firing Squad Synchronization Problem (FSSP) on two-dimensional square arrays is presented and its correctness is demonstrated in detail. Our new solution is time as well as communication optimal (the so-called minimal time 1-bit solution). In addition, it is shown that the technique developed and the results obtained allow also to solve in optimal time & communication FSSP for several other variants of this problem on networks shaped as square grids (with four Generals), square toruses and rings.

This research has been completed while the first author was visiting the Dipartimento di Informatica ed Applicazioni, Università degli Studi di Salerno. Work partially supported by MIUR grant ex-60% 2003 Università di Salerno. The first author is also supported by the grant GAČR, 201/04/1153.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Balzer, R.: An 8-states minimal time solution to the firing squad synchronization problem. Information and Control 10, 22–42 (1967)

    Article  Google Scholar 

  2. Culik, K.: Variations of the firing squad problem and applications. Information Processing Letters 30, 153–157 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  3. Goto, E.: A Minimal Time Solution of the Firing Squad Problem. Lecture Notes for Applied Mathematics, vol. 298, pp. 52–59. Harvard University, Cambridge (1962)

    Google Scholar 

  4. Ilachinski, A.: Cellular Automata: A Discrete Universe. World Scientific, Singapore (2001)

    MATH  Google Scholar 

  5. Imai, K., Morita, K.: Firing squad synchronization problem in reversible cellular automata. Theoretical Computer Science 165, 475–482 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Imai, K., Morita, K., Sako, K.: Firing squad synchronization problem in number-conserving cellular automata. In: Proc. of the IFIP Workshop on Cellular Automata, Santiago, Chile (1998)

    Google Scholar 

  7. Kobayashy, K.: The Firing Squad Synchronization Problem for Two Dimensional Arrays. Information and Control 34, 153–157 (1977)

    Google Scholar 

  8. Kobayashy, K.: On Time Optimal Solutions of the Firing Squad Synchronization Problem for Two-Dimensional Paths. Theoretical Computer Science 259, 129–143 (2001)

    Article  MathSciNet  Google Scholar 

  9. La Torre, S., Parente, M.: Different Time Solutions for the Firing Squad Synchronization Problem on Various Networks, Tech. Rep. DIA - Università degli Studi di Salerno (2001)

    Google Scholar 

  10. Mazoyer, J.: A six states minimal time solution to the firing squad synchronization problem. Theoretical Computer Science 50, 183–238 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  11. Mazoyer, J.: A minimal time solution to the firing squad synchronization problem with only one bit of information exchanged, Laboratoire de l’Information du Parallelisme, Ecole Normale Superieure de Lyon, Rapport n.89-03 (April 1989)

    Google Scholar 

  12. Mazoyer, J.: On optimal solutions to the firing squad synchronization problem. Theoretical Computer Science 168(2), 367–404 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Minsky, M.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)

    MATH  Google Scholar 

  14. Nishimura, J., Sogabe, T., Umeo, H.: A Design of Optimum-Time Firing Squad Synchronization Algorithm on 1-Bit Cellular Automaton Tech. Rep. of IPSJ (2000)

    Google Scholar 

  15. Roka, Z.: The Firing Squad Synchronization Problem on Cayley Graphs. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969, pp. 402–411. Springer, Heidelberg (1995)

    Google Scholar 

  16. Shinar, I.: Two and Three-Dimensional Firing Squad Synchronization Problems. Information and Control 24, 163–180 (1974)

    Article  MathSciNet  Google Scholar 

  17. Szwerinski, H.: Time-Optimal Solution of the Firing-Squad-Synchronization-Problem for n-Dimensional Rectangles with the General at an Arbitrary Position. Theoretical Computer Science 19, 305–320 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  18. Umeo, H., Michisaka, K., Kamikawa, N.: A Synchronization Problem on 1-Bit Communication Cellular Automata. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2657, pp. 492–500. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  19. Waksman, A.: An optimum solution to the firing squad synchronization problem. Information and Control 9, 66–78 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  20. Wolfram, S.: Cellular Automata and Complexity: Collected Papers. Wolfram Research Inc. (1994)

    Google Scholar 

  21. Wolfram, S.: A New Kind of Science. Wolfram Media (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Brno, Slovakia

    Jozef Gruska

  2. Dipartimento di Informatica ed Applicazioni, Università degli Studi di Salerno, Italy

    Salvatore La Torre & Mimmo Parente

Authors
  1. Jozef Gruska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Salvatore La Torre
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mimmo Parente
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, New Zealand

    Cristian S. Calude

  2. Computer Science, Institute of Information and Mathematical Sciences, Massey University Albany, Auckland, New Zealand

    Elena Calude

  3. Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Michael J. Dinneen

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gruska, J., La Torre, S., Parente, M. (2004). Optimal Time and Communication Solutions of Firing Squad Synchronization Problems on Square Arrays, Toruses and Rings. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30550-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24014-3

  • Online ISBN: 978-3-540-30550-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation