Efficient dynamic minimization of word-level DDs based on lower bound computation

Abstract

Word-Level Decision Diagrams (WLDDs), like *BMDs or K*BMDs, have been introduced to overcome the limitations of Binary Decision Diagrams (BDDs), which are the state-of-the-art data structure to represent and manipulate Boolean functions. However, the size of these graph types largely depends on the variable ordering, i.e. it may vary from linear to exponential. In the meantime, dynamic approaches to find a good variable ordering are also known for WLDDs. In this paper we show how these approaches can be accelerated significantly using a combination of a lower bound computation and synthesis operations. In the experiments it turned out that by this technique, the runtime for dynamic minimization can be reduced by more than 40% on average without loss of quality.