On the construction of multiple-valued decision diagrams

Abstract

Decision diagrams are the state-of-the-art representation for logic functions, both binary and multiple-valued. We consider ways to improve the construction of multiple-valued decision diagrams (MDD). Efficiency is achieved through the use of a simple computed table. We compare the use of recursive MIN and MAX as primitive operations in multiple-valued decision diagram construction to the MV-CASE primitive which is a generalization of the if-then-else (ITE) commonly used in binary DD packages. We also consider the use of cyclic negations and complements as MDD edge operations showing that for certain types of functions this approach can lead to significant reduction in MDD node count. They can also reduce the number of primitives that need to be explicitly implemented. Experimental results showing the efficiency of the proposed approaches are given. The direct implementation of MDDs is briefly compared to representing MDDs using a BDD package.