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References
L. Adleman. Two theorems on random polynomial time. In IEEE Sympos. on Foundations of Computer Science, volume 19, pages 75–83, New-York, 1978.
J. L. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity, volume I and II. Springer-Verlag EATCS Monographs, Berlin, 1988–1990. Second Edition for Volume I in 1995.
J. L. Balcázar, M. Hermo, and E. Mayordomo. Characterizations of logarithmic advice complexity classes. Information Processing 92, IFIP Transactions A-12, 1:315–321, 1992.
A.R. Barron. Neural net approximation. In Proc. Seventh Yale Workshop on Adaptive and Learning Systems, pages 69–72, Yale University, 1992.
E.B. Baum and D. Haussler. What size net gives valid generalization? Neural Computation, 1:151–160, 1989.
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. Bull. A.M.S., 21:1–46, 1989.
G.J. Chaitin. On the length of programs for computing finite binary sequences: statistical considerations. J. A.C.M., 16:145–159, 1969.
G. Cybenko. Approximation by superpositions of a sigmoidal function. Math. Control, Signals, and Systems, 2:303–314, 1989.
R.L. Dobrushin and S.I. Ortyukov. Lower bound for the redundancy of self-correcting arrangement of unreliable functional elements. Problems info, Transmission, 13:59–65, 1977.
R.L. Dobrushin and S.I. Ortyukov. Upper bound for the redundancy of self-correcting arrangement of unreliable functional elements. Problems info, Transmission, 13:346–353, 1977.
Y. Finkelstein. Cholinergic Mechanisms of Control and Adaptation in the Rat Septo-Hippocampus under Stress Conditions. PhD thesis, Hebrew University in Jerusalem, Israel, 1994.
J.A. Franklin. On the approximate realization of continuous mappings by neural networks. Neural Networks, 2:183–192, 1989.
S. Franklin and M. Garzon. Neural computability. In O. M. Omidvar, editor, Progress In Neural Networks, pages 128–144. Ablex, Norwood, NJ, 1990.
M. Garzon and S. Franklin. Neural computability. In Proc. 3rd Int. Joint Conf. Neural Networks, volume II, pages 631–637, 1989.
C.L. Giles, B.G. Horne, and T. Lin. Learning a class of large finite state machines with a recurrent neural network. Neural Networks, 1995. In press.
R. Hartley and H. Szu. A comparison of the computational power of neural network models. In Proc. IEEE Conf. Neural Networks, pages 17–22, 1987.
S. Haykin. Neural Networks: A Comprehensive Foundation. IEEE Press, New York, 1994.
J.W. Hong. On connectionist models. On Pure and Applied Mathematics, 41, 1988.
J.E. Hopcroft and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.
K. Hornik. Approximation capabilities of multilayer feedforward networks. Neural Networks, 4:251–257, 1991.
K. Hornik, M. Stinchcombe, and H. White. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks, 3:551–560, 1990.
R.M. Karp and R.J. Lipton. Some connections between uniform and nonuniform complexity classes. In Proceedings of 12th ACM Symp. on Theory of Computing, pages 302–309, 1980.
J. Kilian and H.T. Siegelmann. On the power of sigmoid neural networks. In Proc. Sixth ACM Workshop on Computational Learning Theory, Santa Cruz, July 1993.
G.I. Kirienko. Sintez samokottektiruyshchikhsya skhem iz funktsionalnykh elementov dlya aluchava tastushchego chisla oshibok v skheme. Diskret. Anal., 16:38–43, 1970.
K. Ko. On helping by robust oracle machines. Theoretical Computer Science, 52, 1987, 15–36.
P. Koiran, M. Cosnard, and M. Garzon. Computability with low-dimensional dynamical systems. Theoretical Computer Science, 132:113–128, 1994.
W. Maass, G. Schnitger, and E.D. Sontag. On the computational power of sigmoid versus boolean threshold circuits. In Proc. 32nd IEEE Symp. Foundations of Comp. Sci, pages 767–776, 1991.
M. Matthews. On the uniform approximation of nonlinear discrete-time fading-memory systems using neural network models. Technical Report Ph.D. Thesis, ETH No. 9635, E.T.H. Zurich, 1992.
C.B. Miller and C.L. Giles. Experimental comparison of the effect of order in recurrent neural networks. International Journal of Pattern Recognition and Artificial Intelligence, 7(4):849–872, 1993. Special Issue on Neural Networks and Pattern Recognition, editors: I. Guyon, P.S.P. Wang.
A. A. Muchnik and S. G. Gindikin. The completeness of a system made up of non-reliable elements realizing a function of algebraic logic. Soviet Phys. Dokl, 7:477–479, 1962.
P. Orponen. Neural networks and complexity theory. In Proc. 17th Symposium on Mathematical Foundations of Computer Science, pages 50–61, 1992.
S.I. Ortyukov. Synthesis of asymptotically nonredundant self-correcting arrangements of unreliable functional elements. Problems Inform. Transmission, 13:247–251, 1978.
I. Parberry. Circuit Complexity and Neural Networks. MIT Press, 1994.
A. Paz. Introduction to Probabilistic Automata. Academic Press, New York, 1971.
N. Pippenger. Reliable computation by formulae in the presence of noise. IEEE Trans. Inform. Theory, 34:194–197, 1988.
N. Pippenger. Invariance of complexity measure of networks with unreliable gates. J. ACM, 36:531–539, 1989.
N. Pippenger. Developments in: The synthesis of reliable organisms from unreliable components. In Proc. of symposia in pure mathematics, volume 5, pages 311–324, 1990.
J. B. Pollack. On Connectionist Models of Natural Language Processing. PhD thesis, Computer Science Dept, Univ. of Illinois, Urbana, 1987.
M. M. Polycarpou and P.A. Ioannou. Identification and control of nonlinear systems using neural network models: Design and stability analysis. Technical Report 91-09-01, Department of EE/Systems, USC, Los Angeles, Sept 1991.
C. E. Shannon. A mathematical theory of communication. Bell System Tech J., pages 379–423, 623–656, 1948.
H. T. Siegelmann. On nil: The software constructor of neural networks. Parallel Processing Letters, 6(4):575–582, 1996.
H. T. Siegelmann and E. D. Sontag. Turing computability with neural nets. Appl. Math. Lett., 4(6):77–80, 1991.
H. T. Siegelmann and E. D. Sontag. Analog computation via neural networks. Theoretical Computer Science, 131, 1994. 331–360.
H. T. Siegelmann and E. D. Sontag. On computational power of neural networks. J. Comp. Syst. Sci, 50(1): 132–150, 1995. Previous version appeared in Proc. Fifth ACM Workshop on Computational Learning Theory, pages 440–449, Pittsburgh, July 1992.
H.T. Siegelmann, B.G. Horne, and C.L. Giles. Computational capabilities of recurrent narx neural networks. Technical Report UMIACS-TR-95-12 and CS-TR-3408, Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland, 1995.
E.D. Sontag. Neural nets as systems models and controllers. In Proc. Seventh Yale Workshop on Adaptive and Learning Systems, pages 73–79, Yale University, 1992.
E.D. Sontag. Neural networks for control. In H.L. Trentelman and J.C. Willems, editors, Essays on Control: Perspectives in the Theory and its Applications. Birkhauser, Boston, 1993.
M. Stinchcombe and H. White. Approximating and learning unknown mappings using multilayer feedforward networks with bounded weights. In Proceedings of the International Joint Conference on Neural Networks, IEEE, 1990.
H.J. Sussmann. Uniqueness of the weights for minimal feedforward nets with a given input-output map. Neural Networks, 5:589–593, 1992.
D. Ulig. On the synthesis of self-correcting schemes from functional elements with a small numer of reliable elements. Math. Notes. Acad. Sci. USSR, 15:558–562, 1974.
J. von Neumann. Probabilistic, logics and the synthesis of reliable organisms from unreliable components. In C.E. Shannon and J. McCarthy, editors, Automata Studies. Princeton U. Press, Princeton, NJ, 1956.
N. Wiener. Extrapolation, interpolation, and smoothing of stationary time series. MIT Press, Cambridge, MA, 1949.
D. Wolpert. A computationally universal field computer which is purely linear. Technical Report LA-UR-91-2937, Los Alamos National Laboratory, 1991.
S. Zachos. Robustness of probabilistic computational complexity classes under definitional perturbations. Information and Control, 54:143–154, 1982.
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Siegelmann, H.T. (1998). Neural dynamics with stochasticity. In: Giles, C.L., Gori, M. (eds) Adaptive Processing of Sequences and Data Structures. NN 1997. Lecture Notes in Computer Science, vol 1387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054004
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