Discrete Function Representations Utilizing Decision Diagrams and Spectral Techniques

All discrete function representations become exponential in size in the worst case. Binary decision diagrams have become a common method of representing discrete functions in computer-aided design applications. For many functions, binary decision diagrams do provide compact representations. This work presents a way to represent large decision diagrams as multiple smaller partial binary decision diagrams. In the Boolean domain, each truth table entry consisting of a Boolean value only provides local information about a function at that point in the Boolean space. Partial binary decision diagrams thus result in the loss of information for a portion of the Boolean space. If the function were represented in the spectral domain however, each integer-valued coefficient would contain some global information about the function. This work also explores spectral representations of discrete functions, including the implementation of a method for transforming circuits from netlist representations directly into spectral decision diagrams. ii DEDICATION to Judith and Jeanne iii ACKNOWLEDGEMENTS Sincere thanks are extended to Dr. Bob Reese and Dr. Rainey Little for serving on my committee. Appreciation is also extended to Dr. Alan Mishchenko for his help with the CUDD package. Thanks are also extended to Dr. Jim Harden for the interest he has taken in my studies and to Donna McMurray for all of the assistance she has provided to me. My heartfelt gratitude and upmost regard must be expressed to my advisor, Dr. Mitchell Thornton, whose encouragement and support has made all that I have accomplished possible.