Some remarks about spectral transform interpretation of MTBDDs and EVBDDs

In this paper we give a spectral transform interpretation of AND-EXOR representations of switching functions and related decision diagrams in the vector space over GF(2). The consideration is uniformly extended to the Fourier series-like expressions of functions in the complex vector space and the decision diagrams for integer-valued functions. It is shown that the multi-terminal decision diagrams, MTBDDs, and edge-valued decision diagrams, EVBDDs, for integer-valued functions are derived by using the same sets of basic functions already applied for the decision diagrams attached to some AND-EXOR expressions, but considered over the complex field. The algebraic transform decision diagrams, ATDDs, are considered as the integer counterparts of the functional decision diagrams, FDDs, attached to the algebraic transform in the same way as the FDDs are attached to the Reed-Muller expressions. It is shown that the EVBDDs are the ATDDs in different notation.