Skip to main content
SpringerLink
Log in
Book cover

Unconventional Models of Computation, UMC’2K pp 202–214Cite as

Spatial Computing on Self-Timed Cellular Automata

  • Conference paper

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

Abstract

The huge computational power required to support paradigms of brain-like and evolvable computers in the 21st century will likely be delivered by computers with very homogeneous structures like cellular automata. It is expected that such computers can be manufactured cost-effectively in nanotechnology and will be at least ten orders of magnitude more powerful than current computers. Attempts to do general-purpose computations on cellular automata, however, have not gone beyond simulating Turing Machines on them. This paper proposes more effective ways to exploit the universal computing power of cellular automata. First, by using self-timing of cells, as opposed to synchronous timing, different parts of a cellular automaton can work more independently from each other, so is important to program them in a modular way. Secondly, by laying out programs for cellular automata spatially, the von Neumann communication bottleneck between processing elements and memory elements virtually disappears. Thirdly, by organizing programs as self-timed hierarchical modules, the ease of programming is greatly enhanced. Experiments with hierarchical modular programming are shortly reported.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Abelson, D. Alien, D. Coore, C. Hanson, G. Homsy, T.F. Knight Jr., R. Nagpal, E. Rauch, G.J. Sussman, R. Weiss, “Amorphous Computing”, Communications of the ACM, Vol. 43, No.5, 2000, pp. 74–82.

    Article  Google Scholar 

  2. Amulet group at Univ. of Manchester, “Asynchronous Logic Home Page”, http://www.cs.man.ac.uk/amulet/async/index.html.

  3. E.R. Banks, “Universality In Cellular Automata”, Conf. Record of 1970 IEEE 11th Annual Symp. on Switching and Automata Theory, Santa Monica, California, 28-30 Oct 1970, pp.194–215.

    Google Scholar 

  4. P. Benioff, “Quantum mechanical Hamiltonian models of Turing machines”, Journal of Statistical Physics, Vol. 29,1982, pp. 515–546.

    Article  MathSciNet  MATH  Google Scholar 

  5. “CCA: Continuum Computer Architecture”, http://www.cacr.caltech.edu/CCA/overview.html, 1997.

  6. B. Chappell, “The fine art of IC design”, IEEE Spectrum, Vol. 36, No.7, 1999, pp. 30–34.

    Article  Google Scholar 

  7. E.F. Codd, “Cellular Automata”, New York: Academic Press, 1968.

    Google Scholar 

  8. W. van Dam, “A universal quantum cellular automaton”, 4th Workshop on Physics and Computation, Nov. 1996, In: T. Toffoli, M. Biafore, and J. Leão (ed.), PhysComp96, New England, Complex Systems Institute, 1996, pp. 323–331.

    Google Scholar 

  9. A. DeHon, “Trends toward Spatial Computing Architectures”, Proc. 1999 Int. Solid State Circuits Cont. (ISSCC’99), Feb’99, http://www.cs.berkeley.edu/projects/brass/documents/spatial_isscc99.html.

  10. D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer”, Proc. of the Royal Soc. of London A, Vol. 400, 1985, pp. 97–117.

    Article  MathSciNet  MATH  Google Scholar 

  11. K.E. Drexler, “Nanosystems: Molecular Machinery, Manufacturing, and Computation”, John Wiley and Sons, 1992.

    Google Scholar 

  12. C. Dürr, H.L. Thanh, and M. Santha, “A decision procedure for well-formed quantum linear cellular automata”, Proc. of the 13th Ann. Symp. on Theoretical Aspects of Computer Science, 1996, pp. 2pp81-292.

    Google Scholar 

  13. R. Feynman, “Quantum Mechanical Computers”, Optic News, Vol. 11, 1985, pp. 11–29.

    Article  Google Scholar 

  14. “Special Section on Configurable Computing”, IEEE Transaction on Computers, vol. 48, no. 6, June 1999, pp. 553–639.

    Article  Google Scholar 

  15. T. Isokawa, F. Peper, N. Kouda, N. Matsui, “Computing by Self-Timed Cellular Automata”, International Workshop on Cellular Automata (CA2000), Aug. 2000, Osaka Electro-Communication Univ., H. Umeo and T. Sogabe (eds.), pp. 3–4.

    Google Scholar 

  16. N. Matsui, M. Takai, and H. Nishimura, “A Learning Network Based on Qubit-Like Neuron Model”, Proc. 17th IASTED International Conference on Applied Informatics, Feb. 1999, Innsbruck, Austria, pp. 679–682.

    Google Scholar 

  17. K. Nakamura, “Asynchronous Cellular Automata and their Computational Ability”, Systems, Computers, Controls, Vol. 5, No.5, 1974, pp. 58–66 (Translated from Denshi Tsushin Gakkai Ronbunshi, Vol. 57-D, No. 10, Oct. 1974, pp. 573-580.)

    Google Scholar 

  18. J. von Neumann, Ed: A.W. Burks, “Theory of Self-Reproducing Automata”, University of Illinois Press, 1966.

    Google Scholar 

  19. D.A Patterson, “Microprocessors in 2020”, Scientific American, Sept. 1995, pp. 62–67.

    Google Scholar 

  20. E Peper et al., “Self-Timed Cellular Automata and their Computational Ability”, In preparation, 2000.

    Google Scholar 

  21. A Scarioni D., JA Moreno, “Border Detection in Digital Images with a Simple Cellular Automata Rule”, ACRI’98 Proc. of 3rd Conf. Cellular Automata for Research and Industry, Oct. 1998, pp. 146–156.

    Google Scholar 

  22. J.M. Seminario, J.M. Tour, “Ab Initio Methods for the Study of Molecular Systems for Nanometer Technology: Toward the First-Principles of Molecular Computers”, In: Annals of the New York Academy of Sciences, Vol.852, Molecular Electronics: Science and Technology, (Eds) A. Aviram, M. Ratner, 1998, pp. 68–94.

    Google Scholar 

  23. M. Sipper, “The Artificial Self-Replication Page”, http://lslwww.epfl.ch/pages/research!papers!self_repl/home.html.

    Google Scholar 

  24. M. Sipper, “The Emergence of Cellular Computing”, IEEE Computer, vol. 32, no. 7, 1999, pp. 18–26.

    Article  Google Scholar 

  25. A.R. Smith, “Simple Nontrivial Self-Reproducing Machines”, In C.G. Langton, C. Taylor, J.D. Farmer, and S. Rasmussen (Eds.), Artificial Life II, volume X of SFI Studies in the Sciences of Complexity, pages 709–725, Redwood City, CA, 1992. Addison-Wesley.

    Google Scholar 

  26. I.E. Sutherland, “Micropipelines”, Communications of the ACM, 1989, Vol. 32, No.6, pp. 720–738.

    Article  Google Scholar 

  27. H. Terada, S. Miyata, M. Iwata, “DDMP’s: Self-Timed Super-Pipelined Data-Driven Multimedia Processors”, Proc. of the IEEE, Vol. 87, No.2, 1999, pp. 282–296.

    Article  Google Scholar 

  28. “National and International Technology Roadmaps for Semiconductors”, http://www.sematech.org/public/index.htm.

  29. E. Waingold, M. Taylor, O. Srikrishna, V. Sarkar, W. Lee, J. Kim, M. Frank, P. Finch, R. Barua, J. Babb, S. Amarasinghe, A Agarwal, “Baring it All to Software: Raw Machines”, Computer, Sept. 1997, Vol. 30, No.9, pp. 86-93.

    Google Scholar 

  30. J. Watrous, “On One-Dimensional Quantum-Cellular Automata”, Proc. of the 36th Annual Symp. on Found. of Comp. Science, 1995, pp. 528–537.

    Google Scholar 

  31. E. Winfree, F. Liu, L.A. Wenzler, and N.C. Seeman, “Design and self-assembly of two-dimensional DNA crystals”, Nature, vol. 394, 6 August 1998, pp. 539–544.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Communications Research Laboratory, Ministry of Posts and Telecommunications, Kobe, Japan

    Ferdinand Peper

Authors
  1. Ferdinand Peper
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Solvay Institutes, Free University of Brussels, Belgium

    I. Antoniou

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

    C. S. Calude  & M. J. Dinneen  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London

About this paper

Cite this paper

Peper, F. (2001). Spatial Computing on Self-Timed Cellular Automata. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds) Unconventional Models of Computation, UMC’2K. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0313-4_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0313-4_16

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-415-4

  • Online ISBN: 978-1-4471-0313-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation