Spectral transformation of multiple-valued decision diagrams

This paper describes an algorithm which performs a spectral transformation of a multiple-valued function directly from a decision diagram representation. The spectrum is in turn represented as a decision diagram. The advantage of adding cycle operations to a spectral decision diagram is shown. The complexity of the representation of the spectrum is not fixed as in the matrix case and is shown to be quite compact for many 'practical' functions. Likewise, the execution time of the algorithm is not fixed as it depends on the complexity of the decision diagram representations of the function and the spectrum. This transformation algorithm opens the possibility of broader application of spectral logic design techniques particularly to functions with more variables than could be considered using earlier matrix transformation techniques. The algorithm is applicable to binary functions and to systems of functions. It is readily extended to other transformations with a recursive matrix definition.<>