SPFD: A new method to express functional flexibility

In this paper, we propose a unique way to express functional flexibility by using sets of pairs of functions called "Sets of Pairs of Functions to be Distinguished"(SPFDs) rather than traditional incompletely specified functi ons. This method was very naturally derived from a unique concept for disti nguishing two logic functions, which we explain in detail in this paper, The flexibility represented by an SPFD assumes that the internal logic of a node in a circuit can be freely changed. SPFDs make good use of this assum ption, and they can express larger flexibility than incompletely specified functions in some cases. Although the main subject of this paper is to explain the concept of SPFDs, we also present an efficient method for calculating the functional flexibi lities by SPFDs because the concept becomes useful only if there is an effi cient calculation method for it. Moreover, we present a method to use SPFDs for circuit transformation along with a proof of the correctness of the me thod. We further make a comparison between SPFDs and compatible sets of permissib le functions (CSPFs), which express functional flexibility by incompletely specified functions. As an application of SPFDs, we show a method to optimize LUT (look-up table ) networks and experimental results.