Single-layer perceptron and dynamic neuron implementing linearly non-separable Boolean functions

Authors:
Fangyue Chen;Wenhui Tang;Guanrong Chen
Affiliations:
School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, People's Republic of China;School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, People's Republic of China and Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, People's Re ...;Department of Electronic Engineering, City University of Hong Kong, People's Republic of China
Venue:
International Journal of Circuit Theory and Applications
Year:
2009

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Universal perceptron and DNA-like learning algorithm for binary neural networks: LSBF and PBF implementations

IEEE Transactions on Neural Networks

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Abstract

This paper presents a single-layer perceptron (SLP) scheme with an impulse activation function (IAF) and a dynamic neuron (DN) with a trapezoidal activation function (TAF). Combining with some interesting properties of the offset levels, it is shown that many linearly non-separable Boolean functions can be realized by using only one SLPwIAF or one DNwTAF. In the present work, a few appropriate IAF and TAF are adopted, and the inverse offset level method is used for the design of the SLPwIAF synaptic weights and the DNwTAF templates. The XOR and NXOR Boolean operations with two inputs and all 152 non-separable Boolean functions with three inputs can be easily implemented by one SLPwIAF or one DNwTAF. Finally, the entire set of 152 DNwTAF templates associated with 152 non-separable Boolean functions of three inputs is completely listed. Copyright © 2008 John Wiley & Sons, Ltd.