Abstract
Serious roadblocks have been encountered in several areas of computer application, for example in the solution of intractable (NP-complete) combinatorial problems, or in the simulation of fluid flow. In this talk we will explore two alternatives to the usual kinds of computers, and ask if they provide some hope of ultimately by-passing what appear to be essential difficulties.
Keywords
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. Vergis, K. Steiglitz, B. Dickinson, “The Complexity of Analog Computation,” Mathematics and Computers in Simulation, in press.
D. Farmer, T. Toffoli, S. Wolfram (eds.), Cellular Automata, North-Holland Physics Publishing, Amsterdam, 1984.
K. Preston, Jr., M. J. B. Duff, Modern Cellular Automata, Theory and Applications, Plenum Press, 1984.
K. Steiglitz, R. Morita, “A Multi-Processor Cellular Automaton Chip,” Proc. 1985 IEEE International Conference on Acoustics, Speech, and Signal Processing, Tampa, Florida, March 26–29, 1985.
J. K. Park, K. Steiglitz, W. P. Thurston, “Soliton-Like Behavior in Automata,” Physica D, in press.
F. L. Carter, “The Molecular Device Computer: Point of Departure for Large Scale Cellular Automata,” pp. 175–194 in D. Farmer, T. Toffoli, S. Wolfram (eds.), Cellular Automata, North-Holland Physics Publishing, Amsterdam, 1984.
A. V. Oppenheim, R. W. Schafer, Digital Signal Processing, Prentice-Hall, Englewood Cliffs, N. J., 1975.
E. R. Berlekamp, J. H. Conway, R. K. Guy, Winning Ways for your Mathematical Plays, Vol. 2: Games in Particular, (Chapter 25, “What is Life?”), Academic Press, New York, N. Y., 1982.
F. Nourai, R. S. Kashef, “A Universal Four-State Cellular Computer,” IEEE Trans. on Computers, vol. C-24, no. 8, pp. 766–776, August 1975.
A. C. Scott, F. Y. F. Chu, D. W. McLaughlin, “The Soliton: A New Concept in Applied Science,” Proc. IEEE, vol. 61, no. 10, pp. 1443–1483, October 1973.
R. Hirota, K. Suzuki, “Theoretical and Experimental Studies of Lattice Solitons on Nonlinear Lumped Networks,” Proc. IEEE, vol. 61, no. 10, pp. 1483–1491, October 1973.
A. Church, “An Unsolvable Problem of Elementary Number Theory,” Amer. J. Math., vol. 58, pp. 345–363, 1936. (Reprinted in [13].)
M. Davis, The Undecidable, Raven Press, Hewlett, NY, 1965.
R.P. Feynman, “Simulating physics with computers,” Internat. J. Theoret. Phys., vol. 21, pp. 467–488, 1982.
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman & Co., San Francisco, CA, 1979.
D.S. Johnson, “The NP-completeness Column: an Ongoing Guide,” J. Algorithms, vol.4, pp. 87–100, 1983.
A. Jackson, Analog Computation, McGraw-Hill, New York, NY, 1960.
W. Karplus and W. Soroka, Analog Methods, 2nd. ed., McGraw-Hill, New York, NY, 1959.
D. Plaisted, “Some Polynomial and Integer Divisibility Problems are NP-Hard,” Proc. 17th Ann. Symp. on Foundations of Computer Science, pp. 264–267, 1976.
A. M. Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proc. London Math. Soc., Series 2, vol. 42, pp. 230–265, 1936–1937;
A. M. Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proc. London Math. Soc., Series 2, vol. 43, pp. 544–546, 1937. (Reprinted in [13].)
K. Steiglitz, I. Kamal, A. Watson, “Embedding Computation in One-Dimensional Automata by Phase Coding Solitons,” Tech. Rept. No. 15, Dept. of Computer Science, Princeton University, Princeton NJ 08544, Nov. 1985.
N. Islam, K. Steiglitz, “Phase Shifts in Lattice Solitons, and Applications to Embedded Computation,” in preparation.
A. K. Dewdney, “On the Spaghetti Computer and other Analog Gadgets for Problem Solving,” in the Computer Recreations Column, Scientific American, vol. 250, no. 6, pp. 19–26, June 1984.
A. K. Dewdney, “On the Spaghetti Computer and other Analog Gadgets for Problem Solving,” in the Computer Recreations Column, Scientific American, vol. 250, no. 6, pp. 19–26, Sept. 1984, June 1985, and May 1985, the last also containing a discussion of one-dimensional computers.
J. B. Salem, S. Wolfram, “Thermodynamics and Hydrodynamics with Cellular Automata,” unpublished manuscript, November 1985.
U. Frisch, B. Hasslacher, Y. Pomeau, “A Lattice Gas Automaton for the Navier Stokes Equation,” Preprint LA-UR-85–3503, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, 1985.
S. Wolfram, “Cellular Automaton Fluids 1: Basic Theory,” preliminary manuscript, Institute for Advanced Study, Princeton, NJ 08540, 1986.
S. R. Sternberg, “Computer Architectures Specialized for Mathematical Morphology,” pp. 169–176 in Algorithmic ally Specialized Parallel Computers, L. Snyder, L. H. Jamieson, D. B. Gannon, H. J. Siegel (eds.), Academic Press, 1985.
S. Kugelmass, K. Steiglitz, in progress.
C. H. Goldberg, “Parity Filter Automata,” in preparation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Kluwer Academic Publishers
About this chapter
Cite this chapter
Steiglitz, K. (1988). Two Non-Standard Paradigms for Computation: Analog Machines and Cellular Automata. In: Skwirzynski, J.K. (eds) Performance Limits in Communication Theory and Practice. NATO ASI Series, vol 142. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2794-0_11
Download citation
DOI: https://doi.org/10.1007/978-94-009-2794-0_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7757-6
Online ISBN: 978-94-009-2794-0
eBook Packages: Springer Book Archive