Neural Networks – A Model of Boolean Functions

This paper deals with the representation of Boolean functions using artificial neural networks and points out three important results. First, using a polynomial as transfer function, a single neuron is able to represent a non-monotonous Boolean function. Second, the number of inputs in the neural network can be decreased if the binary values of the Boolean variables are encoded. This approach simplifies significantly the necessary number of neurons in the artificial neural network. Finally, an algorithm to compute the minimal number of neurons was developed. The lower bound, calculated by this algorithm, corresponds to a suggested structure of artificial neural networks. An example shows, how such a simple artificial neural network may represent a Boolean function.