Eecient Spectral Coeecient Calculation Using Circuit Output Probabilities

Many problems in the eld of digital logic may be solved more eeciently in the spectral domain than in the Boolean domain. However, the primary drawback of spectral techniques is the large complexity associated with the calculation of the spectrum of a Boolean function. We present a new method for the computation of a spectral coeecient that has a complexity equal to O(j E j) where j E j is the number of edges in a binary decision diagram characterizing the circuit. This result is especially signiicant for techniques that require the calculation of only a few spectral coeecients since it allows the computations to be accomplished very eeciently and does not require storage resources for a large number values. Furthermore, this method holds for any general spectral transform and does not require the transformation matrix to be recursively deened or sparse.