On the size of multiple-valued decision diagrams

Abstract

The worst-case number of nodes is considered for decision diagrams for general and totally-symmetric multiple-valued functions. We present upper bounds on the number of nodes and then show the bounds are exact by showing how to construct decision diagram of that size. We also show that cyclic edge negations do not reduce the worst case size as much as might be anticipated. Finally, we show that functions exist which have exponential size with respect to one radix, but have linear size with respect to a different radix.