Dynamic Minimization of Bi-Kronecker Functional Decision Diagrams

Abstract

A recently proposed canonical representation called Bi-Kronecker Functional Decision Diagrams (BKFDDs) utilizes the classical decompositions (the Shannon and Davio decompositions) and their biconditional variants, and hence can be seen as a generalization of some existing decision diagrams: BDDs, FDDs, KFDDs and BBDDs. However, the size of BKFDDs for a Boolean function is very sensitive to variable orders with decomposition types (ODTs). Therefore, identifying a good ODT is of paramount importance for BKFDDs. In this paper, we propose four dynamic minimization algorithms for BKFDDs, which encapsulate smart strategies to search for a good ODT in a dynamic way. The experiments have been carried out on four influential benchmarks: ISCAS89, MCNC, ITC99 and EPFL, and the experimental results show that the proposed group sifting algorithms for BKFDDs are very effective and can produce BKFDDs with smaller size than state-of-the-art packages of DDs.