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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)433-451
Journal / PublicationInternational Journal of Circuit Theory and Applications
Issue number3
Publication statusPublished - Apr 2009


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 SLPwLAF 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.

Research Area(s)

  • Cellular neural network (CNN), Dynamic neuron (DN), Impulsive activation function (IAF), Linearly separable Boolean function (LSBF), Non-LSBF, Single-layer perceptron (SLP), Trapezoidal activation function (TAF)