How many fixed-polarity reed-muller expressions there are, English

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How many fixed-polarity reed-muller expressions there are

For functions in Exercise 3.8, determine the fixed polarity arithmetic expressions, and show that the FPRM- repressions can be derived from them by recalculating the coefficients modulo 2 and replacing the operations of the addition and subtraction by EXOR.

Exercise 3.8

How many Fixed-polarity Reed-Muller expressions there are for functions of n = 3 variables? Determine all them for the function given by the SOP-expression

and compare their complexities in terms of the number of non-zero coefficients.

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