On the Average Path Length in Decision Diagrams of Multiple-Valued Functions

• Authors: J. T. Butler;T. Sasao
• Venue: ISMVL '03 Proceedings of the 33rd International Symposium on Multiple-Valued Logic
• Year: 2003

We consider the path length in decision diagramsfor multiple-valued functions. This is an importantmeasure of decision diagram, since this models thetime needed to evaluate the function. We focus onthe average path length (APL), which is the sumof the path lengths over all ssignments of valuesto the variables divided by the number of assignments. First, we show multiple-valued functionin which the APL is markedly affected by the orderof variables. We show upper and lower bounds onthe longest path length in decision diagram ofmultiple-valued function. Next, we derive the APLfor individual functions, the MAX, ALL_MAX, andMODSUM functions. We show that the latter twofunctions achieve the lower and upper bound on theAPL over all n-variable r-valued functions. Finally,we derive the average of the APL for two sets offunctions, symmetric functions and all functions.