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Compact representations of switching functions pro- vide for simplied realizations of logic networks. Recent advent of digital technology and VLSI raised a considerable interest in polynomial expressions for switching functions. Complexity of these expressions is estimated through the number of product terms. For a given function and the selected class of polyno- mial expressions, the number of products can be reduced by a suitable selection of polarities for switching variables, which results in Fixed Polarity Polynomial Expressions (FPPEs). This paper proposes a method for optimization of polyno- mial representation of switching functions. The method ex- ploits the notion of dual polarity of switching variables and takes advantages of a simple relationship between two FPPEs for dual polarities. Calculation of FPPEs is performed along the extended dual polarity route so that each FPPE is calcu- lated from its extended dual polarity FPPE. Conversion from one FPPE to another is carried out by using one-bit check, which ensures the eciency of the method. The proposed method can be applied to arbitrary polynomial expressions providing that the corresponding transform matrix has the Kronecker product structure.

Dual polarity in optimization of polynomial representation of switching functions