Index Generation Functions

Tsutomu Sasao received B.E., M.E., and Ph.D. degrees in Electronics Engineering from Osaka University, Osaka Japan, in 1972, 1974, and 1977, respectively. He has held faculty/research positions at Osaka University, Japan; IBM T. J. Watson Research Center, Yorktown Height, NY; the Naval Postgraduate School, Monterey, CA; and Kyushu Institute of Technology, Iizuka, Japan. Now, he is a Professor of Department of Computer Science, Meiji University, Kawasaki, Japan. His research areas include logic design and switching theory, representations of logic functions, and multiple-valued logic. He has published more than 10 books on logic design including, Logic Synthesis and Optimization (1993), Representation of Discrete Functions (1996), Switching Theory for Logic Synthesis (1999), Logic Synthesis and Verification (2002), Progress in Applications of Boolean Functions (2010), Memory-Based Logic Synthesis (2011), and Applications of Zero-suppressed Decision Diagrams (2015).He has served Program Chairman for the IEEE International Symposium on Multiple-Valued Logic (ISMVL) many times. Also, he was the Symposium Chairman of the 28th ISMVL held in Fukuoka, Japan in 1998. He received the NIWA Memorial Award in 1979, Takeda Techno-Entrepreneurship Award in 2001, and Distinctive Contribution Awards from IEEE Computer Society MVL-TC for papers presented at ISMVLs in 1986, 1996, 2003, 2004, 2013, and 2018. He has served an associate editor of the IEEE Transactions on Computers. He is a Life Fellow of the IEEE. Mitchell A. (Mitch) Thornton received the BS degree in electrical engineering from Oklahoma State University in Stillwater, OK, in 1985, the MS degree in electrical engineering from the University of Texas-Arlington in Arlington, Texas, in 1990, the MS degree in computer science from Southern Methodist University in 1993, and the PhD degree in computer engineering from Southern Methodist University in 1995. He was a senior electronic systems engineer at E-Systems, Inc. in Greenville, TX from 1986 through 1991. He was employed as a design engineer at Cyrix Corporation from 1992 through 1993. He has served as a full-time faculty member in the University of Arkansas from 1995 to 1999, and Mississippi State University from 1999 to 2002. Currently he is the Cecil H. Green Chair of Engineering and Professor at Southern Methodist University in the Computer Science and Engineering Department, and by courtesy, in the Electrical Engineering Department. He also serves as the Technical Director of the Darwin Deason Institute for Cyber Security.

Preface
Acknowledgments
Introduction
Applications
Definitions and Basic Properties
Index Generation Functions and Their Realizations
Minimization of Primitive Variables
Linear Transformations of Input Variables
Iterative Reduction of Compound Variables
Irreducible Index Generation Function
SAT-Based Method to Find Linear Transformations
Statistical Approach
Realization Using Four IGUs
References on Index Generation Functions
Conclusions
Bibliography
Author's Biography
Index