A novel approach for mapping of a boolean function using artificial neural network
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Date
2017-07
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G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
Boolean functions have enormous importance in the field of Computer Engineering. These functions are important not only because of the fact that computer hardware architecture is based on them but also because of ever-increasing automation using devices like programmable logical controllers that utilize such functions in ladder programming. Another aspect of the importance of Boolean functions is the ability to transform any number to binary form for the purpose of any kind of processing or analysis of the data. Owing to this fact, various methods for representation of Boolean functions have been suggested in the literature. The input-output relationship for the devices based on Boolean functions can be mapped using trained artificial neural networks. Artificial Neural Network (ANN) is an intelligent tool with parallel computational capability. Conventional ANN once designed needs to be trained using iterative training process. The proposed method for mapping of Boolean functions is advantageous because of its generality and ease of implementation. This method is based on a novel neural architecture known as Pi-Sigma neuron model. Although Pi-Sigma neuron model is complex but the proposed new Pi-Sigma neuron model named as Simplified Pi-Sigma neuron model reduces the complexity and makes the learning process simple and non-iterative. While the conventional neuron models have summation operation for aggregation, the proposed neuron model has multiplication as well as summation operations for representing aggregation of the dendritic inputs. Incorporation of the multiplication operation along with the summation operation is based on some biological evidences as observed by researchers in the field of computational neuroscience. As any Boolean function can be represented in terms of sum of products, the proposed neuron model is capable of representing any Boolean function because of its inherent nature of performing multiplication operations before performing summation operations. The advantage with this method is that it does not require a long process of iterations for training. Weights and biases are directly calculated by presenting the training data in a single stroke. The proposed model works primarily for Boolean functions, but it can be extended to any kind of functions by using the conversion of number systems along with this method of functional mapping.
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