ETDD-based synthesis of two-dimensional cellular arrays for multi-output incompletely specified Boolean functions

Complex terms are logic expressions which can be mapped directly to cell arrays of cellular architecture devices such as Atmel 6000 series FPGAs. The paper presents an approach to the generation of complex terms for multi-output incompletely specified Boolean functions using EXOR ternary decision diagrams ETDDs. The expansions, Shannon, positive Davio and negative Davio, inherent in ETDDs, are employed to generate complex terms. While traversing the ETDD can be accomplished in a simple and efficient way for completely specified functions, the manipulation of ETDDs with don´t care terms becomes very complex because the three expansions require different evaluations of the function. The changes made to the function due to don´t cares in each expansion are analysed, and an approximation algorithm is presented with its applications to the minimisation of functions composed of complex terms.