Implementing size-optimal discrete neural networks require analog circuitry

This paper starts by overviewing results dealing with the approximation capabilities of neural networks, as well as bounds on the size of threshold gate circuits. Based on a constructive solution for Kolmogorov´s superpositions we will show that implementing Boolean functions can be done using neurons having an identity transfer function. Because in this case the size of the network is minimised, it follows mat size-optimal solutions for implementing Boolean functions can be obtained using analog circuitry. Conclusions and several comments on the required precision are ending the paper.