Advanced BDD Optimization

by Rudiger Ebendt, Görschwin Fey, Rolf Drechsler

Overview

VLSI CADhas greatly benefited from the use of reduced ordered Binary Decision Diagrams (BDDs) and the clausal representation as a problem of Boolean Satisfiability (SAT), e.g. in logic synthesis, ver- cation or design-for-testability. In recent practical applications, BDDs are optimized with respect to new objective functions for design space exploration. The latest trends show a growing number of proposals to fuse the concepts of BDD and SAT. This book gives a modern presentation of the established as well as of recent concepts. Latest results in BDD optimization are given, c- ering different aspects of paths in BDDs and the use of efficient lower bounds during optimization. The presented algorithms include Branch— and Bound and the generic A -algorithm as efficient techniques to - plore large search spaces.— The A -algorithm originates from Artificial Intelligence (AI), and the EDA community has been unaware of this concept for a long time. Re-— cently, the A -algorithm has been introduced as a new paradigm to explore design spaces in VLSI CAD. Besides AI search techniques, the book also discusses the relation to another field of activity bordered to VLSI CAD and BDD optimization: the clausal representation as a SAT problem.

Product Details

ISBN-13:	9780387254531
Publisher:	Springer US
Publication date:	08/23/2005
Edition description:	2005
Pages:	222
Product dimensions:	6.14(w) x 9.13(h) x 0.02(d)

Table of Contents

Preface. 1. Introduction. 2. Preliminaries. 2.1. Notation. 2.2. Boolean Functions. 2.3. Decomposition of Boolean Functions. 2.4. Reduced Ordered Binary Decision Diagrams.- 3. Exact node Minimization. 3.1. Branch and Bound Algorithm. 3.2. A*-Based Optimization. 3.3. Summary.- 4. Heuristic node Minimization. 4.1. Efficient Dynamic Minimization. 4.2. Improved Lower Bounds for Dynamic Reordering. 4.3. Efficient Forms of Improved Lower Bounds. 4.4. Combination of Improved Lower Bounds with Classical Bounds. 4.5. Experimental Results. 4.6. Summary.- 5. Path Minimization. 5.1. Minimization of Number of Paths. 5.2. Minimization of Expected Path Length. 5.3. Minimization of Average Path Length. 5.4. Summary.- 6. Relation between SAT and BDDS. 6.1. Davis-Putnam Procedure. 6.2. On the Relation between DP Procedure and BDDs. 6.3. Dynamic Variable Ordering Strategy for DP Procedure. 6.4. Experimental Results. 6.5. Summary.- 7. Final Remarks. References. Index.