Efficient algorithms for the calculation of Walsh spectrum from OBDD and synthesis of OBDD from Walsh spectrum for incompletely specified Boolean functions

An algorithm converting ordered binary decision diagram (OBDD) representation of Boolean functions to its Walsh spectrum has been developed. The decomposition of Walsh spectral coefficients in terms of cofactors of Boolean functions resembling Shannon decomposition has been proposed. Based on the above decomposition, a second new algorithm is presented to synthesize ordered binary decision diagram directly from Walsh spectrum of Boolean functions.