By: Ingo Wegener, Peter Hammer (Editor)

Sorry, the book that you are looking for is not available right now.

We did a search for other books with a similar title, however there were no matches. You can try selecting from a similar category, click on the author's name, or use the search box above to find your book.

Click on the Google Preview image above to read some pages of this book!

Finite functions (in particular, Boolean functions) play a fundamental role in computer science and discrete mathematics. This book describes representations of Boolean functions that have small size for many important functions and which allow efficient work with the represented functions. The representation size of important and selected functions is estimated, upper and lower bound techniques are studied, efficient algorithms for operations on these representations are presented, and the limits of those techniques are considered. This book is the first comprehensive description of theory and applications. Research areas like complexity theory, efficient algorithms, data structures, and discrete mathematics will benefit from the theory described in this book. The results described within have applications in verification, computer-aided design, model checking, and discrete mathematics. This is the only book to investigate the representation size of Boolean functions and efficient algorithms on these representations.

Preface	p. ix
Introduction	p. 1
Branching Programs (BPs) and Binary Decision Diagrams (BDDs)	p. 1
Motivations from Theory	p. 5
Motivations from Applications	p. 6
On the Inherent Complexity of Some Problems	p. 11
Survey	p. 14
Exercises	p. 17
BPs and Decision Trees (DTs)	p. 19
BPs, Circuits, Formulas, and Space	p. 19
Lower Bound Techniques for BPs	p. 26
Upper Bound Techniques for BPs	p. 30
Algorithms on BPs	p. 35
DTs	p. 37
Exercises and Open Problems	p. 43
Ordered Binary Decision Diagrams (OBDDs)	p. 45
OBDDs	p. 45
OBDDs and Deterministic Finite Automata (DFAs)	p. 49
Efficient Algorithms on OBDDs	p. 51
Breadth-First Manipulation of OBDDs	p. 57
Parallel Computers and OBDDs	p. 60
Incompletely Specified Boolean Functions	p. 61
Exercises and Open Problems	p. 66
The OBDD Size of Selected Functions	p. 69
OBDDs and Communication Complexity	p. 69
Read-Once Projections	p. 71
Storage Access	p. 74
Addition	p. 75
Multiplication	p. 77
Squaring and Division	p. 80
Symmetric Functions	p. 81
General Threshold Functions	p. 82
Functions with Short Disjunctive Normal Forms (DNFs)	p. 84
The Hidden Weighted Bit Function	p. 84
Read-Once Formulas	p. 87
Selected Functions on Matrices	p. 88
Exercises and Open Problems	p. 90
The Variable-Ordering Problem	p. 93
The Variable-Ordering Problem	p. 93
Random Functions	p. 94
Nice, Ugly, and Ambiguous Functions	p. 96
The Complexity of the Variable-Ordering Problem	p. 99
The Computation of Optimal Variable Orderings	p. 100
Heuristics for the Computation of Good Variable Orderings	p. 105
Changing the Variable Ordering	p. 107
Reordering Techniques	p. 116
Transformations of Boolean Functions	p. 121
Exercises and Open Problems	p. 125
Free BDDs (FBDDs) and Read-Once BPs	p. 129
Definition and Upper Bound Techniques	p. 129
Lower Bound Techniques	p. 133
Algorithms on FBDDs	p. 143
Algorithms on G-FBDDs	p. 146
Search Problems	p. 155
Exercises and Open Problems	p. 158
BDDs with Repeated Tests	p. 161
The Landscape between OBDDs and BPs	p. 161
Upper Bound Techniques	p. 163
Efficient Algorithms and NP-Hardness Results	p. 168
Lower Bound Techniques for (1, +k)-BPs	p. 174
Lower Bound Techniques for Oblivious BDDs	p. 177
Lower Bound Techniques for k-BPs	p. 188
Lower Bounds for Depth-Restricted BPs	p. 192
Exercises and Open Problems	p. 193
Decision Diagrams (DDs) Based on Other Decomposition Rules	p. 195
Zero-Suppressed Binary Decision Diagrams (ZBDDs)	p. 195
Ordered Functional Decision Diagrams (OFDDs)	p. 202
Ordered Kronecker Functional Decision Diagrams (OKFDDs)	p. 211
Exercises and Open Problems	p. 212
Integer-Valued DDs	p. 215
Multivalued Decision Diagrams (MDDs)	p. 215
Multiterminal BDDs (MTBDDs)	p. 216
Binary Moment Diagrams (BMDs)	p. 220
Hybrid Decision Diagrams (HDDs)	p. 225
Edge-Valued Binary Decision Diagrams (EVBDDs)	p. 225
Edge-Valued Binary Moment Diagrams (*BMDs)	p. 230
Exercises	p. 235
Nondeterministic DDs	p. 237
Different Modes and Models of Nondeterminism	p. 237
Upper Bound Techniques	p. 241
Lower Bound Techniques	p. 245
Partitioned OBDDs	p. 251
Algorithms for EXOR-OBDDs	p. 261
Exercises and Open Problems	p. 268
Randomized BDDs and Algorithms	p. 271
Randomized Equivalence Tests	p. 271
Randomized BDD Variants	p. 274
Probability Amplification	p. 276
Throw the Coins First	p. 280
Upper Bound Results	p. 281
Efficient Algorithms and Hardness Results	p. 287
Lower Bounds for Randomized OBDDs and k-OBDDs	p. 289
Lower Bounds for Randomized FBDDs and k-BPs	p. 293
Exercises and Open Problems	p. 299
Summary of the Theoretical Results	p. 303
Algorithmic Properties	p. 303
Bounds for Selected Functions	p. 305
Complexity Landscapes	p. 309
Applications in Verification and Model Checking	p. 313
Verification of Combinational Circuits	p. 313
Verification of Sequential Circuits	p. 321
Symbolic Model Checking	p. 326
Further CAD Applications	p. 331
Two-Level Logic Minimization	p. 331
Multilevel Logic Synthesis	p. 339
Functional Simulation	p. 343
Test Generation	p. 345
Timing Analysis	p. 346
Technology Mapping	p. 349
Synchronizing Sequences	p. 352
Boolean Unification	p. 353
Applications in Optimization, Counting, and Genetic Programming	p. 357
Integer Programming	p. 357
Network Flow	p. 361
Counting Problems	p. 366
Genetic Programming	p. 370
Bibliography	p. 379
Index	p. 403
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780898714586
ISBN-10: 0898714583
Series: Monographs on Discrete Mathematics & Applications S.
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 418
Published: 1st July 2000
Dimensions (cm): 22.8 x 15.2  x 2.7
Weight (kg): 0.749