Introduction

Abstract

Binary Decision Diagrams (BDDs) as a data structure for Boolean functions were already introduced by Lee in 1959 [93] and later on popularized by Akers [2] . Furthermore, under the name of Branching Programs they were intensively studied in theoretical computer science (see e.g. [156, 102] ). Nevertheless, it took until 1985/86, when Bryant introduced the concept of Ordered Binary Decision Diagrams and demonstrated that BDDs in this restricted form, later on in this book also called BDDs for simplicity, allow canonical representation and efficient manipulation of Boolean functions [25]. Within the following years the importance of BDDs for VLSI CAD was realized by several groups and an increasing number of BDD algorithms and successful applications were reported [100, 67, 34, 27, 10] . In 1990 the first BDD packages, SW tools for the representation and manipulation of BDDs, became available [19, 107] . Since then, new generation BDD packages offering significant improvements, e.g. with respect to minimization methods, have been published [99, 147] . Today BDDs have become the state-of-the-art data structure in VLSI CAD generally accepted as providing a good compromise between conciseness of representation and efficiency of manipulation. With increasing number of applications, also in non CAD areas, classical methods to handle BDDs are being improved, e.g. dynamic reordering methods, originally introduced in [68] and [126], have been refined and today are essential in many applications.