Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

9010985. The work of M. Garzon was partially supported by National Science Grants DCR-8602319 and CCR-9010985.


REFERENCES

Aberth, O. ( 1980). Computable analysis, New York: McGraw Hill.

Alon, N., Dewdney, A. K., & Ott, T. J. ( 1991). "Efficient simulation of finite automata by neural nets". Journal of the Association for Computing Machinary, 38( 2), 495-514.

Berlekamp, E. R., Conway, J. H., & Guy, R. K. ( 1982). Winning ways for your mathematical plays, New York: Academic. Vol. 2 (Chapter 25).

Bishop, E. ( 1985). Constructive analysis, Berlin: Springer-Verlag.

Blum, L., Shub, M., & Smale, S. ( 1989). "On a theory of computation over the real numbers; NP- completeness, recursive functions and universal machines". Bulletin of the American Mathematical Society, 21, 1-46.

Botelho, F., & Garzon, M. ( 1991). "Global dynamics in neural networks", III Proceedings of the International Joint Conference on Neural Networks ( Seattle, WA) Vol. 1 (pp. 541-547). Also in Complex Systems, 5( 4), 401-413.

Botelho, F., & Garzon, M. ( 1994a). "Boolean neural nets are observable". Theoret. Computational Science, 134, 51-61. Corrigendum forthcoming (see Garzon (1995), Theorem 9.43).

Botelho, F., & Garzon, M. ( 1994b). "Generalized shadowing properties". Journal of Random and Computational Dynamics, 2( 2), 145-164.

Brouwer, L. E. J. ( 1913). "Intuitionism and Formalism". Bulletin of the American Mathematical Society. (Trans., A. Drosden) 20, 81.

Chartrand, G., & Lesniak, L. ( 1986). Graphs and digraphs ( 2nd ed.). Cole, CA: Wadsworth and Brooks.

Ciesinger, J. ( 1988). "Neural nets as powerful as game of life" (as powerful as Turing machines). SIGACT News, 19, 46-7.

Cosnard, M., Garzon, M., & Koiran., P. ( 1993). "Computability properties of low-dimensional dynamical systems". Symposium on Theoretical Aspects of Computer Science' 93, [Ext. Abstract]. Lecture Notes in Computer Science, 665, New York: Springer-Verlag. Final version in Theoret. Computational Science, 132, 113-128.

Coxeter, H. S. M., & Moser, W. O. ( 1972). Generators and relations for discrete groups. New York: Springer-Verlag.

Cybenko, G. ( 1989). "Approximation by superpositions of a sigmoidal function". Math. Control, Signals and Systems, 2, 303-314.

Devaney, R. L. ( 1986). An introduction to chaotic dynamical systems, Reading, MA: Addison-Wesley.

Fogelman-Soulié, F., Robert, Y., & Tchuente M. ( 1987). "Automata networks in computer science", Manchester university. Press.

Franklin, S., & Garzon, M. ( 1988a). "Global dynamics of neural networks". Complex Systems, 2, 692- 701.

Franklin, S., & Garzon, M. ( 1988b). "Neural network implementation of Turing machines". IEEE 2nd International Conference on Neural Networks, November. Poster session.

Franklin, S., & Garzon, M. ( 1991). "Neural computability". In O. M. Omidvar (Ed.). Progress in neural networks (Vol. 1, Chap. 6, pp. 127-145). Norwood, NJ: Albex.

Franklin, S., & Garzon, M. ( 1992). "On stability and solvability (or when does a neural network solve a problem?)". Minds and Machines, 2, 71-83.

Funahashi, K. ( 1989). "On the approximate realization of continuous mappings by neural networks". Neural Networks, 2, 183-192.

Garzon, M. ( 1992). "Graphical words and languages". In M. Ito. (Ed.). Proceeding of the International Conferences on Words, Languages, and Combinatorics (pp. 160-178). Singapore: Word Publishing.

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