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Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references and index.

1. Introduction to zero-suppressed decision diagrams / Alan Mishchenko -- Chapter summary -- 1.1 Introduction -- 1.2 Definitions -- 1.2.1 BDD and ZDD reduction rules -- 1.3 Comparing BDDs and ZDDs -- 1.3.1 Boolean functions -- 1.3.2 Sets of subsets -- 1.3.3 Cube covers -- 1.4 Basic ZDD procedures -- 1.4.1 Procedures working with functions -- 1.4.2 Procedures working with covers -- 1.4.3 Generic structure of a recursive ZDD procedure -- 1.5 Manipulation of sets -- 1.5.1 A case study of the CUDD source code -- 1.6 Manipulation of cube covers -- 1.7 Mixed ZDD/BDD applications -- 1.7.1 Computation of the set of all primes -- 1.7.2 Computation of an irredundant SOP -- 1.8 A list of published ZDD applications -- 1.9 Conclusions -- 1.10 Acknowledgements -- 1.11 Appendix A -- 1.12 Appendix B -- 1.13 Exercises -- References --

2. Efficient generation of prime implicants and irredundant sum-of-products expressions / Tsutomu Sasao -- Chapter summary -- 2.1 Logical expressions -- 2.2 Monotone and unate functions -- 2.3 Prime implicants -- 2.4 Generation of all the prime implicants -- 2.5 Generation of irredundant sum-of-products expressions -- 2.6 Morreale's algorithm -- 2.7 Conclusion and comments -- 2.8 Exercises -- References --

3. The power of enumeration-BDD/ZDD-based algorithms for tackling combinatorial explosion / Shin-ichi Minato -- Chapter summary -- 3.1 Introduction -- 3.2 BDDs/ZDDs and graph enumeration -- 3.3 Frontier-based method -- 3.3.1 Knuth's SimPath algorithm -- 3.3.2 Frontier-based method for various problems -- 3.3.3 Recent topics on the path enumeration problem -- 3.4 Conclusion -- 3.5 Exercises -- References --

4. Regular expression matching using zero-suppressed decision diagrams / Shinobu Nagayama -- Chapter summary -- 4.1 Introduction -- 4.2 Preliminaries -- 4.2.1 Regular expressions and finite automaton -- 4.2.2 Binary decision diagrams -- 4.3 BDDs and ZDDs for NFAs -- 4.3.1 Representations of NFAs using BDDs -- 4.3.2 Representations of NFAs using ZDDs -- 4.4 Matching method using BDDs and ZDDs -- 4.4.1 Regular expression matching method using BDDs [39] -- 4.4.2 Regular expression matching method using ZDDs -- 4.5 Experimental results -- 4.5.1 Comparison of the number of nodes -- 4.5.2 Comparison of computation time -- 4.6 Conclusion and comments -- AcknowledgmentS -- 4.7 Exercises -- References --

A. Solutions -- Authors' and editors' biographies -- Index.

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A zero-suppressed decision diagram (ZDD) is a data structure to represent objects that typically contain many zeros. Applications include combinatorial problems, such as graphs, circuits, faults, and data mining. This book consists of four chapters on the applications of ZDDs. The first chapter by Alan Mishchenko introduces the ZDD. It compares ZDDs to BDDs, showing why a more compact representation is usually achieved in a ZDD. The focus is on sets of subsets and on sum-of-products (SOP) expressions. Methods to generate all the prime implicants (PIs), and to generate irredundant SOPs are shown. A list of papers on the applications of ZDDs is also presented. In the appendix, ZDD procedures in the CUDD package are described. The second chapter by Tsutomu Sasao shows methods to generate PIs and irredundant SOPs using a divide and conquer method. This chapter helps the reader to understand the methods presented in the first chapter. The third chapter by Shin-Ichi Minato introduces the "frontier-based" method that efficiently enumerates certain subsets of a graph. The final chapter by Shinobu Nagayama shows a method to match strings of characters. This is important in routers, for example, where one must match the address information of an internet packet to the proper output port. It shows that ZDDs are more compact than BDDs in solving this important problem. Each chapter contains exercises, and the appendix contains their solutions.

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Title from PDF title page (viewed on December 23, 2014).