Optimal expression for fixed polarity dual Reed-Muller forms.
Khalid Faraj, A.E.A. Almaini · Research Output (Edinburgh Napier University) · 2007
An algorithm for converting between products of sum (POS) and fixed polarity dual Reed-Muller (FPDRM) is proposed in this paper. This algorithm is used to compute the coefficients of POS from FPDRM directly from the truth table of POS. This algorithm is also used to compute the coefficients of POS from FPDRM. Another algorithm is presented in this paper to find the optimal polarity.The most popular minimization criterion of the dual Reed-Muller form is obtained by exhaustive search of all the polarity vectors. Another exhaustive method for dual Reed-Muller expressions is presented. This algorithm will find the optimal polarity among the 2" different polarities for large n-variable functions, without generating all of the polarity sets. This algorithm is based on separating the truth vector of POS and the use of sparse techniques, which will lead to the optimal polarity. Time efficiency and computing speed are thus achieved in this technique.