An Ashenhurst disjoint and non-disjoint decomposition of logic functions in Reed-Muller spectral domain

The paper deals with the problems of logic function decomposition in Reed-Muller spectral domain. The Ashenhurst decompositions are considered with respect to implementation of logic functions in LUT based FPGA. The decompositions are executed on Positive Polarization Reed-Muller spectrum of decomposed functions. The problems of input variables assigning to the free set, bounded set and common set during logic function disjoint and non-disjoint decomposition were addressed. A method of finding profitable common variables set (from the point of view of non-disjoint decomposition) is based on utilisation of Logic Differential Calculus and authors experiences. The decomposition is carried out in Reed-Muller spectral domain because the Boolean differentials are easy calculated from Reed-Muller form of logic function which is obtained as reverse Reed-Muller transform.