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Simulations between programs as cellular automata

  • Howard A. Blair
  • Fred Dushin
  • Polar Humenn
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1265)

Abstract

We present cellular automata on appropriate digraphs and show that any covered normal logic program is a cellular automaton. Seeing programs as cellular automata shifts attention from classes of Herbrand models to orbits of Herbrand interpretations. Orbits capture both the declarative, model-theoretic meaning of programs as well as their inferential behavior. Logically and intentionally different programs can produce orbits that simulate each other. Simple examples of such behavior are compellingly exhibited with space-time diagrams of the programs as cellular automata. Construing a program as a cellular automaton leads to a general method for simulating any covered program with a Horn clause program. This means that orbits of Horn programs are completely representative of orbits of covered normal programs.

Keywords

logic program cellular automaton orbit simulation 

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References

  1. [Ap90]
    Apt, K. R. “Logic Programming” in Handbook of Theoretical Computer Science, J. van Leeuwen, ed., Elsevier, 1990, pp. 494–574.Google Scholar
  2. [B-H96]
    Blair, H.A., Jagan Chidella, Fred Dushin, Audrey Ferry & Polar Humenn. “A Continuum of Discrete Systems” Annals of Mathematics and Artificial Intelligence, to appear.Google Scholar
  3. [BMS95]
    Blair, H.A., Marek, W. and Schlipf, J. “The Expressiveness of Locally Stratified Programs”, Annals of Mathematics and Artificial Intelligence, 15(1995)209–229.Google Scholar
  4. [Fi94]
    Fitting, M. “Metric methods, three examples and a theorem” Journal of Logic Programming volume 21, 1994, pp 113–127.Google Scholar
  5. [Ga70]
    Gardner, Martin. “The Fantastic Combinations of John Conway's New Solitaire Game ‘Life',” Scientific American 223(4) (April, 1970), pp. 120–123.Google Scholar
  6. [Ha82]
    Halmos, P.R. A Hilbert Space Problem Book Springer-Verlag, Graduate Texts in Mathematics no. 19, 1982.Google Scholar
  7. [Ke55]
    Kelly, J.L. General Topology, Van Nostrand, 1955, Reprinted by Springer-Verlag, Graduate Texts in Mathematics, no. 27.Google Scholar
  8. [Mi96]
    Mitchell, Melanie (1996). Computation in Cellular Automata: A Selected Review. Santa Fe Institute Working Paper 96-09-074.Google Scholar
  9. [NS93]
    Nerode, A. and R. Shore, Logic for Applications, Springer-Verlag, 1993.Google Scholar
  10. [Pr88]
    Przymusinski, T. “On the Declarative Semantics of Deductive Databases and Logic Programs,” in Foundations of Deductive Databases and Logic Programming, Jack Minker, ed. Morgan-Kaufmann, Los Altos, CA. 1988Google Scholar
  11. [Ro67]
    Rogers, H. Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York, 1967.Google Scholar
  12. [Sh91]
    Shepherdson J. C. “Unsolvable Problems for SLDNF-Resolution”, Journal of Logic Programming, 10(1), 1991, pp. 19–22Google Scholar
  13. [Su87]
    Subrahmanian, V.S. On the Semantics of Quantitative Logic Programs, Proc. 4th IEEE Symp. on Logic Programming, pps 173–182, Computer Society Press. Sept. 1987.Google Scholar
  14. [TM87]
    Toffoli, Tommaso & Norman Margolis. Cellular Automata Machines: a new environment for modeling. MIT Press, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  1. 1.School of Computer and Information ScienceSyracuse UniversitySyracuseUSA
  2. 2.Black Watch Technology, Inc., 2-212 Case CenterSyracuse UniversitySyracuseUSA

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