The Role of the Observer in Uniform Systems

  • Tommaso Toffoli
Part of the NATO Conference Series book series (NATOCS, volume 5)

Abstract

Starting from models of particular interest for the physicist, there has evolved in the course of years, with different emphasis and varying degrees of abstraction, a vast literature of mathematical structures known collectively as “general dynamical systems [1].” In this area of investigation, the analysis of particular systems has often led to the study of more general media, i.e., of “host” systems in which a variety of “guest” systems can be embedded. Great conceptual economy and, at the same time, great flexibility, is achieved by considering media that are arbitrarily extended and uniform. For example, while a differential equation of the form x = -f(x) describes a single, isolated oscillator, partial differential equations such as those of the electromagnetic field in a homogeneous medium may be made to describe, with a suitable choice of initial conditions, systems of waves of many kinds, including particle-like “packets” of waves. In the discrete domain, a particular sequential process realized by a specialized piece of hardware, may be reproduced by assigning appropriate initial conditions (stored program) to a more uniformly structured, general-purpose computer.

Keywords

Cellular Automaton Uniform System Uniform Medium Universal Turing Machine General Dynamical System 
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.

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References

  1. 1.
    K. S. Sibirsky, Introduction to Topological Dynamics, Leyden, The Netherlands, 1975.Google Scholar
  2. 2.
    J. von Neumann, Theory of Self-Reproducing Automata (ed. A. W. Burks), Urbana, Illinois, 1966.Google Scholar
  3. 3.
    T. Toffoli, Topics in Cellular Automata Mechanics, Ph.D. Thesis, University of Michigan, Computer & Communication Sciences Dept. (to appear).Google Scholar
  4. 4.
    M. Gardner, “Mathematical Games,” Sci. Amer., 223:4 (1970), pp. 120–123.CrossRefGoogle Scholar
  5. 5.
    H. Yamada and S. Amoroso, “Tessellation Automata,” Information and Control, 14 (1969), pp. 299–317.CrossRefGoogle Scholar
  6. 6.
    E. F. Codd, Cellular Automata, Academic Press, 1968.Google Scholar
  7. 7.
    E. R. Banks, Information Processing and Transmission in Cellular Automata, Ph.D. Thesis, MIT, 1971.Google Scholar
  8. 8.
    A. R. Smith, Cellular Automata Theory, Tech. Report No. 2, Stanford Electrical Laboratory, 1969.Google Scholar
  9. 9.
    A. G. Vitushkin, Theory of Transmission and Processing of Information, Pergamon Press, 1961.Google Scholar
  10. 10.
    T. Toffoli, Computation- and Construction-Universality of Reversible Cellular Automata, Tech. Report No. 192, University of Michigan, Computer and Communication Sciences Dept., 1976 (to appear in J. Comp. Sys. Sci.).Google Scholar
  11. 11.
    R. Laing, “Automaton Introspection,” J. Comp. Sys. Sci., 13 (1976), pp. 172–182.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • Tommaso Toffoli
    • 1
  1. 1.The Logic of Computers Group, Computer and Communication, Sciences DepartmentUniversity of MichiganAnn ArborUSA

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