Abstract
We formally introduced a new model of computations the RealRAM and its parallel counterpart the RealPRAM. We study the relationship between these models, classical computational models and two recently proposed parallel machine models, the real machine from Blum, Shub and Smale and the analog neural networks from Siegelman and Sontag. We propose a classification using simulations by dynamical systems. We also generalise the NC class and P-complete problems to real computations.
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J.L. Balcázar, J. Diáz, and J. Gabarró. Structural Complexity I. EATCS monographs on theoretical computer science. Springer-Verlag, 1988.
L. Blum, M. Shub, and S. Smale. On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines. Bulletin of the American Mathematical Society, 21(1):1–46, July 1989.
M. Cosnard and A. Ferreira. On the real power of loosely coupled parallel architectures. Parallel Processing Letters, 1(2):103–112, 1991.
M. Cosnard, M. Garson, and P. Koiran. Computability properties of low-dimensional systems. In Proceedings of STACS'9S, Lecture notes in computer science to appear. Springer Verlag, 1993.
F. Cucker and F. Rossello. On the complexity of some problems for the Blum, Shub and Smale model. In Proceedings of Latin'92, Lecture notes in computer science, pages 530–545. Springer Verlag, 1992.
R.M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. Handbook of Theoretical Computer Science, Vol. A Algorithms and complexity, pages 870–941, 1990.
P. Koiran. On the relations between dynamical systems and boolean circuits. Research Report in preparation, LIP, Ecole Normale Supérieure de Lyon, 1992.
B. Martin. A universal parallel random-access machine based on cellular automata. Research Report, LIP, Ecole Normale Supérieure de Lyon, 1992.
F.P. Preparata and Shamos M.I. Computational Geometry. Springer, 1985.
H. T. Siegelman and E. D. Sontag. Neural networks with real weights: analog computational complexity. COLT92 and SYCON Report 92-05, Rutgers University, September 1992.
H. T. Siegelman and E. D. Sontag. On the computational power of neural nets. In Proc. Fifth ACM Workshop on Computational Learning Theory, July 1992.
P. van Emde Boas. Machine models and simulations. Handbook of Theoretical Computer Science, Vol. A Algorithms and complexity, pages 3–66, 1990.
F.F. Yao. Computational geometry. Handbook of Theoretical Computer Science, Vol. A Algorithms and complexity, pages 345–389, 1990.
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© 1993 Springer-Verlag Berlin Heidelberg
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Cosnard, M., Koiran, P. (1993). Relations between models of parallel abstract machines. In: Meyer, F., Monien, B., Rosenberg, A.L. (eds) Parallel Architectures and Their Efficient Use. Nixdorf 1992. Lecture Notes in Computer Science, vol 678. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56731-3_5
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DOI: https://doi.org/10.1007/3-540-56731-3_5
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