Number of spectral coefficients necessary to identify a class of Boolean functions

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Abstract
It is well known that only n+1 spectral coefficients, the Chow or modified-Chow parameters, are necessary to uniquely define any given linearly separable (threshold) function. It is here shown that n+1 coefficients only are necessary to define a much wider class of Boolean functions, namely all Boolean functions which can be realised from a threshold-logic core function with pre- and postlinear-translation operations. The use of n+1 spectral coefficients as a fault signature for all such functions is therefore possible.

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