Abstract
This chapter proposes spectral decision diagrams (STDDs), that are graphical representations of spectral transforms of switching functions and integer-valued functions. Binary decision diagrams (BDDs) and functional decision diagrams (FDDs) are graphical representations for switching functions and their Reed-Muller transforms, respectively. Multi-terminal decision diagrams (MTBDDs), arithmetic transform decision diagrams (ACDDs), and Walsh transform decision diagrams (WDDs) are graphical representations for integer-valued functions, their arithmetic transforms, and their Walsh transforms, respectively. This chapter shows that an STDD represents a function and its spectral transform at the same time. As for n-bit adders, ACDDs and WDDs require O(n) nodes while MTBDDs require O(2 n ) nodes. As for n-bit multipliers, ACDDs and WDDs require O(n 2) nodes while MTBDDs require O(4 n ) nodes.
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