Average and worst case number of nodes in decision diagrams of symmetric multiple-valued functions

We derive the average and worst case number of nodes in decision diagrams of r-valued symmetric functions of n variables. We show that, for large n, both numbers approach n/sup r//rl. For binary decision diagrams (r=2), we compute the distribution of the number of functions on n variables with a specified number of nodes. Subclasses of symmetric functions appear as features in this distribution. For example, voting functions are noted as having an average of n/sup 2//6 nodes, for large n, compared to n/sup 2//2, for general binary symmetric functions.