Highly efficient exhaustive search algorithm for optimizing canonical Reed-Muller expansions of boolean functions

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Abstract
A new method is presented for calculating fixed polarity Reed-Muller expansions from the boolean minterms. Direct transformation equations of Reed-Muller expansions with polarity are derived. A highly efficient and flexible exhaustive search algorithm is presented which can obtain an optimum polarity more quickly if a sub-optimum polarity is obtained first. Also exact formulae are presented for optimum polarities for any three-variable logic function.

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