Efficient minimization of multiple-valued decision diagrams for incompletely specified functions

This paper addresses the problem of finding a small size Multiple-Valued Decision Diagram (MDD) representation of an incompletely specified multiple-valued function. Optimal MDD representation improves performance and flexibility of many applications in logic design and multiple-valued circuit synthesis. We introduce an algorithm which incorporates a new operation on incompletely specified MDDs, called fusion. The diagram is optimized by dynamic variable ordering, graph compaction and minimization. During the optimization the structure of the underlying MDD is modified in a way that only specified values are represented while don´t cares are ignored. The results on multiple-valued as well as binary benchmarks with don´t cares are given to demonstrate the efficiency and robustness of the algorithm.