This book contributes new results of research in the Boolean domain, many of which are related to important real-life applications that will support readers in solving their scientific and practical tasks.

Ongoing digitalization leads to ever more applications with growing complexity. The digits of such applications are usually encoded by Boolean variables due to their simplicity as only two values are used. However, an exponentially growing number of vectors of Boolean variables can negate this simplicity. This leads to challenges created by advancing progress in the Boolean domain with a wide field of applications. Many new theoretical insights, concepts, methods, and tools contribute to this progress. Some of these new results are presented in this book.

Networked computers are an important resource that facilitates the interchange of information. Data must be protected against attacks while being computed, stored, and transmitted. Encryption of data is an effective approach to protect data against several types of attacks. Boolean functions are used to realize both encryption and decryption procedures. The three chapters of Part I contribute the results of new research, which can increase cyber security.

A critical issue is the exponential complexity of computation in the Boolean domain. Part II shows one example of high practical importance, where the exponential timecomplexity has been reduced to polynomial complexity.

Out of the huge number of practical applications, Part III addresses an application belonging to the main challenges human welfare is facing at this time. It provides a solution that controls renewable energy sources using distributed agents.

The last part of this book is related to future technologies. An alternative approach to computation motivates the change from classical logic circuits to quantum circuits. Quantum computing is based on completely different paradigms. The two chapters of Part IV explore these new paradigms and demonstrate a mapping from matrices of complex numbers to ternary vector lists representing Boolean functions.

Keywords:

Boolean problems, theoretical insights, concepts, methods, tools, cyber security, complexity, application to control renewable energy, future technology, quantum circuits.

Bernd Steinbach studied Information Technology at the Chemnitz University of Technology, Germany, graduating with an MSc, a PhD, and a DSc techn. He obtained his Habilitation from the Faculty of Electrical Engineering of the same institution in 1991. From 1992 to 2017, he served as Full Professor of Computer Science at the Freiberg University of Mining and Technology, Germany, while he is also the Head of the Steinbeis-Transfer-Center “Logic Systems”. He is the co-author and editor of 20 books, and has published more than 280 book chapters and papers. He received the Barkhausen Award from the University of Technology Dresden in 1983.

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