Hybrid Reed-Muller Haar Representations of Logic Functions

摘要

Spectral transformations of logic functions, like Reed-Muller or Haar transformations, have numerous applications in digital logic design, AND-EXOR synthesis, testing, communications etc. Recently the Reed-Muller Haar (RMH) transform defined for different algebraic structures has been presented. In practice, different classical transforms may serve as a way in constructing new so called hybrid transforms allowing to exploit good features especially required in certain applications. Here we propose a combination of two transforms, namely, Reed-Muller and Reed-Muller Haar, which we call hybrid Reed-Muller-Haar transform (HybrRMH). As one of many potential applications of this transform, we consider the reduction of the number of nonzero coefficients in HybrRMH expressions. The extension of HybrRMH to multiple-valued case, in particular, ternary case is considered as well.