The complexity of Boolean functions in the Reed–Muller polynomials class
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This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of n variables whose complexity (in terms of the number of terms) coincides with value. We investigate the properties of functions and propose their schematic realization on elements AND, XOR, and NAND.
KeywordsBoolean function symmetric Boolean function Reed–Muller polynomial Zhegalkin polynomial polynomial complexity Shannon functions Boolean derivative triangle method logical scheme
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