The paper describes a method of representing an n-dimensional array of rational expressions as an (n + 1)-dimensional array of scalars and shows how this representation readily supports the implementation of various common array operations. A feature of the representation is that it can take advantage of memorysaving schemes for encoding large, sparse scalar arrays using multi-terminal binary d...

Variable reordering is the main approach to minimize the size of Ordered Binary Decision Diagrams. But despite the huge effort spent, up to now, to design different reordering heuristics, their performance often does not meet the needs of the applications. In many OBDD-based computations, the time cost for reordering dominates the time spent by the computa-

Binary Decision Diagrams and Its Variable Ordering for Disjoint Network Manoj Singhal Associate professor, Department of Information Technology, Accurate Institute of Management & Technology, Greater Noida (U.P.), India, Email: [email protected] Girish Sharma Associate Professor, Department of Computer Applications, Bhai Parmanand Institute of Business Studies, New Delhi Email: gkps1...

In many real-life problems, we are often faced with manipulating discrete structures. Manipulation of large discrete structures is one of the most important problems in computer science. For this purpose, a family of data structures called decision diagrams is used. The origin of the decision diagrams is binary decision diagram (BDD) proposed by Bryant in 1980s. BDD is a data structure to repre...

The Sentential Decision Diagram (SDD) is a recently proposed representation of Boolean functions, containing Ordered Binary Decision Diagrams (OBDDs) as a distinguished subclass. While OBDDs are characterized by total variable orders, SDDs are characterized by dissections of variable orders, known as vtrees. Despite this generality, SDDs retain a number of properties, such as canonicity and a p...

The application of Binary Decision Diagrams (BDDs) as an efficient approach for the minimization of Disjoint Sums-of-Products (DSOPs) is discussed. DSOPs are a starting point for several applications. The use of BDDs has the advantage of an implicit representation of terms. Due to this scheme the algorithm is faster than techniques working on explicit representations and the application to larg...

| Reduced ordered binary decision diagrams (OBDDs) are nowadays the state-of-the-art representation scheme for Boolean functions in Boolean manipulation. Recent results have shown that it is possible to use the more general concept of free binary decision diagrams (FBDDs) without giving up most of the useful computational properties of OBDDs, but possibly reducing the space requirements conside...

We identify a new representation of propositional knowledge bases, the Sentential Decision Diagram (SDD), which is interesting for a number of reasons. First, it is canonical in the presence of additional properties that resemble reduction rules of OBDDs. Second, SDDs can be combined using any Boolean operator in polytime. Third, CNFs with n variables and treewidth w have canonical SDDs of size...

Branching programs (b. p.'s) or decision diagrams are a general graph-based model of sequential computation. The b. p.'s of polynomial size are a nonuniform counterpart of LOG. Lower bounds for diierent kinds of restricted b. p.'s are intensively investigated. An important restriction are so called k-b. p.'s, where each computation reads each input bit at most k times. Although, for more restri...

Binary and multivalued decision diagrams are closely related to dynamic programming (DP) but differ in some important ways. This paper makes the relationship more precise by interpreting the DP state transition graph as a weighted decision diagram and incorporating the state-dependent costs of DP into the theory of decision diagrams. It generalizes a well-known uniqueness theorem by showing tha...