Solving the XOR and parity N problems using a single universal binary neuron

Soft Computing

Volumn 12, Issue 3, 2008, Pages 215-222

  Aizenberg, Igor ^a  

^a TEXAS A AND M UNIVERSITY TEXARKANA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; LEARNING ALGORITHMS; NEURAL NETWORKS; NEURONS; PROBLEM SOLVING;

UNIVERSAL BINARY NEURON;

SOFT COMPUTING;

EID: 38949173125     PISSN: 14327643     EISSN: 14337479     Source Type: Journal    
DOI: 10.1007/s00500-007-0204-9     Document Type: Article

References (18)

1. Aizenberg IN (1985) Model of the element with complete functionality. Izvestia Akademii Nauk SSSR, Technicheskaia Kibernetika (J Comput Syst Sci Int) (2):188-191 (in Russian)
2. Aizenberg IN (1991) The universal logical element over the field of the complex numbers, Kibernetika (Cybern Syst Anal), (3):116-121 (in Russian)
3. Aizenberg I, Moraga C (2007) Multilayer feedforward neural network based on multi-valued neurons (MLMVN) and a backpropagation learning algorithm. Soft Comput 11(2):169-183
4. Aizenberg I, Aizenberg N, Vandewalle J (2000) Multi-valued and universal binary neurons: Theory, learning, applications. Kluwer, Boston, Dordrecht, London
5. Aizenberg NN, Aizenberg IN (1991) Model of the neural network basic elements (Cells) with universal functionality and various hardware implementations. In: Proceedings of the 2nd international conference "Microelectronics for Neural Networks", Kyrill & Methody Verlag, Munich, pp 77-83
6. Aizenberg NN, Aizenberg IN (1992) CNN based on multi-valued neuron as a model of associative memory for gray-scale images. In: Proceedings of the 2nd IEEE international workshop on cellular neural networks and their applications, Technical University Munich, Germany, 14-16 October 1992, pp 36-41
7. Aizenberg NN, Aizenberg IN (1993) Quickly converging learning algorithms for multi-level and universal binary neurons and solving of the some image processing problems. In: Mira J, Cabestany J, Prieto A (eds). Lecture notes in computer science, vol 686. Springer, Berlin, pp 230-236
8. Aizenberg NN, Ivaskiv Yu L (1977) Multiple-valued threshold logic. Naukova Dumka Publisher House, Kiev (in Russian)
9. Aizenberg NN, Ivaskiv Yu L, Pospelov DA (1971) About one generalization of the threshold function Doklady Akademii Nauk SSSR (The Reports of the Academy of Sciences of the USSR), 196:1287-1290 (in Russian)
10. Dertouzos ML (1965) Threshold logic: A synthesis approach. The MIT Press, Cambridge
11. Fung H, Li LK (2001) Minimal feedforward parity networks using threshold gates. Neural Comput 13:319-326
12. Haykin S (1999) Neural networks: A comprehensive foundation, 2nd edn. Prentice Hall, Englewood Cliffs
13. Hebb DD (1949) The organization of behavior. Wiley, New York
14. Minsky LM, Papert AS (1968) Perceptrons: An introduction to computational geometry, expanded edition. MIT Press, Cambridge
15. Mizutani E, Dreyfus SE, Jang J-SR (2000) On dynamic programming-like recursive gradient formula for alleviating hidden-node saturation in the parity problem. In: Proceedings of the international workshop on intelligent systems resolutions - the 8th Bellman Continuum, Hsinchu, Taiwan, pp 100-104
16. Rosenblat F (1962) Principles of neurodynamics: Perceptrons and the theory of brain mechanisms. Spartan, New York
17. Suzuki K, Horiba I, Sugie N (2003) Neural edge enhancer for supervised edge enhancement from noisy images. IEEE Trans Pattern Anal Mach Intell 25(12):1582-1596
18. Wang H-M, Zhao J-Y, Guo S-D, Yu D-H (2002) A new kind of shadow detector based on CNN-UBN. In: Proceedings of the 1st IEEE international conference on machine learning and cybernetics, Beijing, 4-5 November 2002, pp 69-72