Mixed-radix MVL Function Spectral and Decision Diagram Representation

Discrete finite-valued functions are increasingly important in applications involving automation and control. In particular, it is evident that industry is focusing on Systems-on-a-Chip (SoC) where the integration of analog (infinite-valued) and digital (binary-valued) circuits must co-exist. As designers struggle with these interfacing issues, it is natural to consider the intermediate circuits that can be modeled as multi-valued, discrete logic-level circuits. This viewpoint is not unprecedented as such principles have been used for at least the past twenty years in telecommunications protocols. If an analogous approach is considered in control systems implemented in Integrated Circuit (IC) designs, it is proposed that spectral analysis may provide an important role and efficient methods for computing such mixed-radix function spectra are described here. These methods are formulated as transformations of word-level decision diagrams representing the underlying arithmetic expressions and can be implemented as graph traversal algorithms. The theoretical foundation of the spectral transform of a mixed-radix function is presented and the equivalence of the resulting spectrum and the spectrum of a Cayley graph is shown.