Quaternion groups versus dyadic groups in representations and processing of switching functions

In this paper we compare effects of two different domain groups for switching functions to the efficiency of calculation of spectral transforms (ST) representations and the complexity of Decision diagrams (DDs) representations. Dyadic groups and quaternion groups are assumed for domain groups for switching functions. We compared space and time complexity in calculation of STs representations through FFT. DDs are compared an terms of their basic characteristics, the depth, the width, and the size. The area of a DD, defined as the product of size and width, and for word-level DDs, the ratio between the number of non-terminal and constant nodes are discussed as another characteristics of DDs dependent on the domain groups. It as shown that the quaternion groups have advantages in processing of large switching functions. When number of variables grows, these advantages increases.