On some representations of Boolean functions. Application to the theory of switching elements nets

We consider three representations of a Boolean function, two of them in the real field and one in a Galois field modulo-2. By using these representations, an arbitrary Boolean function of n variables can always be expanded as a power series on the Boolean variables cut off to the n-th degree (n-form). Such representations are particularly useful for a unified treatment of the dynamics of a net of switching elements.