Invited paper. Boolean matrix representation for the conversion of minterms to Reed–Muller coefficients and the minimization of Exclusive-OR switching functions

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Abstract
Two new efficient algorithms are proposed to convert the minterms of a switching function to the coefficients of its Reed-Muller polynomial with fixed polarities. The conversion procedure is based on the use of boolean matrix representation. The first algorithm is applied to generate all the generalized Reed-Muller expansions of the related switching function and select the optimum solution from them. The second algorithm is applied to generate directly the minimal generalized Reed-Muller expansion for a given switching function without undertaking all possible fixed polarity realizations. The two algorithms can also be applied to generate the minimal Exclusive-OR realization in fixed polarity for the incompletely specified functions. Two fast and efficient computer simulations for the proposed algorithms have been developed using BASIC programming language, these computer programs accept the number of the function variables and the minterms of a switching function and return the minimal Reed-Muller expansion in fixed polarity. Both algorithms are suitable for large variable functions for hand and computer simulations. This paper contains demonstration examples based on the proposed algorithms.

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