Binary Decision Diagrams and Applications for VLSI CAD

Symbolic Boolean manipulation using binary decision diagrams (BDDs) has been successfully applied to a wide variety of tasks, particularly in very large scale integration (VLSI) computer-aided design (CAD). The concept of decision graphs as an abstract representation of Boolean functions dates back to the early work by Lee and Akers. In the last ten years, BDDs have found widespread use as a concrete data structure for symbolic Boolean manipulation. With BDDs, functions can be constructed, manipulated, and compared by simple and efficient graph algorithms. Since Boolean functions can represent not just digital circuit functions, but also such mathematical domains as sets and relations, a wide variety of CAD problems can be solved using BDDs.
`Binary Decision Diagrams and Applications for VLSI CAD provides valuable information for both those who are new to BDDs as well as to long time aficionados.' -from the Foreword by Randal E. Bryant.
`Over the past ten years ... BDDs have attracted the attention of many researchers because of their suitability for representing Boolean functions. They are now widely used in many practical VLSI CAD systems. ... this book can serve as an introduction to BDD techniques and ... it presents several new ideas on BDDs and their applications. ... many computer scientists and engineers will be interested in this book since Boolean function manipulation is a fundamental technique not only in digital system design but also in exploring various problems in computer science.' - from the Preface by Shin-ichi Minato.

1 Introduction.- 1.1 Background.- 1.2 Outline of the Book.- 2 Techniques of BDD Manipulation.- 2.1 Binary Decision Diagrams.- 2.2 Logic Operations.- 2.3 Memory Management.- 2.4 Attributed Edges.- 2.5 Implementation and Experiments.- 2.6 Conclusion.- 3 Variable Ordering for BDDS.- 3.1 Properties of the Variable Ordering.- 3.2 Dynamic Weight Assignment Method.- 3.3 Minimum-Width Method.- 3.4 Conclusion.- 4 Representation of Multi-Valued Functions.- 4.1 Boolean Functions with Don’t Care.- 4.2 Representation of Boolean-to-Integer Functions.- 4.3 Remarks and Discussions.- 5 Generation of Cube Sets from BDDS.- 5.1 Previous Works.- 5.2 Generation of Prime-Irredundant Cube Sets.- 5.3 Experimental Results.- 5.4 Conclusion.- 6 Zero-Suppressed BDDS.- 6.1 BDDs for Sets of Combinations.- 6.2 Zero-Suppressed BDDs.- 6.3 Manipulation of ZBDDs.- 6.4 Unate Cube Set Algebra.- 6.5 Implementation and Applications.- 6.6 Conclusion.- 7 Multi-Level Logic Synthesis Using ZBDDS.- 7.1 Implicit Cube Set Representation.- 7.2 Factorization of Implicit Cube Set Representation.- 7.3 Implementation and Experimental Results.- 7.4 Conclusion.- 8 Implicit Manipulation of Polynomials Based on ZBDDS.- 8.1 Representation of Polynomials.- 8.2 Algorithms for Arithmetic Operations.- 8.3 Implementation and Experiment.- 8.4 Application for LSI CAD.- 8.5 Conclusion and Remarks.- 9 Arithmetic Boolean Expressions.- 9.1 Introduction.- 9.2 Manipulation of Arithmetic Boolean Expressions.- 9.3 Applications.- 9.4 Conclusion.- 10 Conclusions.- References.