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A Continuous Model of Computation

MAY 01, 1999
Physicists should consider an alternative to the Turing‐machine model of computation.

DOI: 10.1063/1.882660

Joseph F. Traub

A central dogma of computer science is that the Turing‐machine model is the appropriate abstraction of a digital computer. Physicists who’ve thought about the matter also seem to favor the Turing‐machine model. For example, Roger Penrose devoted some 60 pages of a book to a description of this abstract model of computation and its implications. I argue here that physicists should consider the real‐number model of computation as more appropriate and useful for scientific computation.

References

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  2. 2. A. M. Turing, Proc. London Math. Soc. 42, 230 (1937).https://doi.org/PLMTAL

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  5. 5. J. von Neumann, Collected Works, V. A. Taub, ed., Macmillan, New York (1963).

  6. 6. L. Blum, F. Cucker, M. Shub, S. Smale, Complexity and Real Computation, Springer‐Verlag, New York (1998).

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  8. 8. A. S. Nemirovski, D. B. Yudin, Problem Complexity and Method Efficiency in Optimization, Wiley‐Interscience, New York (1983).

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  10. 10. E. Novak, Deterministic and Stochastic Error Bound in Numerical Analysis, Lecture Notes in Mathematics, No. 1349, Springer‐Verlag, New York (1988).

  11. 11. L. Plaskota, Noisy Information and Computational Complexity, Cambridge U. P., Cambridge, England (1996).

  12. 12. S. Paskov, J. F. Traub, J. Portfolio Management, 22, 113 (1995).

  13. 13. I. Sloan, H. Woźniakowski, J. Complexity 14, 1 (1998).https://doi.org/JOCOEH

  14. 14. A. Papageorgiou, J. F. Traub, Computers in Physics 11, 574 (1997).

  15. 15. B. Keister, Computers in Physics 10, 119 (1996).

  16. 16. G. W. Wasilkowski, H. Wozniakowski, J. Math. Phys. 37, 2071 (1996).https://doi.org/JMAPAQ

  17. 17. M. B. Pour‐El, J. I. Richards, Computability in Analysis and Physics, Springer‐Verlag, New York (1988).

  18. 18. A. G. Werschulz, Numer. Func. Anal. 9, 945 (1987).

More about the Authors

Joseph F. Traub. Columbia University, New York City.

This Content Appeared In
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Volume 52, Number 5

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