Problems and new solutions in the boolean domain / edited by Bernd Steinbach.

Includes bibliographical references (pages [384]-422) and index.

I Methods, Algorithms, and Programs -- General methods -- Efficient calculations -- II Applications -- Several aspects of security -- Exploration of properties -- III Towards Future Technologies -- Reversible circuits -- Quantum circuits.

A vector space method for Boolean switching networks /Mitchell A. Thornton -- Solving combinatorial problems using Boolean equations /Christian Posthoff, Bernd Steinbach -- Simplification of extremely large expressions /Ben Ruijl, Jos Vermaseren, Aske Plaat, Jaap van den Herik -- A novel approach of polynomial expansions of symmetric functions /Danila A. Gorodecky -- XBOOLE-CUDA : fast calculations of large Boolean problems on the GPU /Bernd Steinbach, Matthias Werner -- Efficient computing of the Gibbs dyadic derivatives /Radomir S. Stanković, Dusan Gajić, Suzana Stojković, Milos Radmanović -- Understanding the performance of randomized algorithms /Jan Schmidt, Rudolf B. Blažek, Petr Fišer -- Fast network intrusion detection systems with high maintainability /Shinobu Nagayama, Shinʼichi Wakabayashi -- Utilization of Boolean functions in cryptography /Chunhui Wu, Bernd Steinbach -- Minimization of ESOP forms for secure computation /Stelvio Cimato, Valentina Ciriani, Matteo Moroni -- On the relationship of Boolean function spectra and circuit output probabilities /Micah A. Thornton, Mitchell A. Thornton -- ROBDD-based computation of special sets with RelView applications /Rudolf Berghammer, Stefan Bolus -- Multiple-valued functions with bent Reed-Muller spectra /Claudio Moraga, Milena Stanković, Radomir S. Stanković -- A framework for reversible circuit complexity /Mathias Soeken, Nabila Abdessaied, Rolf Drechsler -- Gate count minimal reversible circuits /Jerzy Jegier, Paweł Kerntopf -- The synthesis of a quantum circuit /Alexis de Vos, Stijn de Baerdemacker -- Universal two-qubit quantum gates /Md. Mazder Rahman, Gerhard W. Dueck.

The Internet of Things is a great new challenge for the development of digital systems. In addition to the increasing number of classical unconnected digital systems, more people are regularly using new electronic devices and software that are controllable and usable by means of the internet. All such systems utilize the elementariness of Boolean values. A Boolean variable can carry only two different Boolean values: FALSE or TRUE (0 or 1), and has the best interference resistance in technical systems. However, a Boolean function exponentially depends on the number of its variables. This exponential complexity is the cause of major problems in the process of design and realization of circuits. According to Moore's Law, the complexity of digital systems approximately doubles every 18 months. This requires comprehensive knowledge and techniques to solve complex Boolean problems. This book summarizes both new problems and solutions in the Boolean domain in solving such issues.Part 1 describes powerful new approaches in solving exceptionally complex Boolean problems. Efficient methods contribute to solving problems of extreme complexity. New algorithms and programs utilize the huge number of computing cores of the Graphical Processing Unit and improve the performance of calculations by several orders of magnitude. Part 2 represents several applications of digital systems. Due to the crucial role of the internet, both solutions and open problems regarding the security of these systems are discussed. The exploration of certain properties of such systems leads to a number of efficient solutions, which can be reused in a wide field of applications. Part 3 discusses the scientific basis of future circuit technologies, investigating the need for completely new design methods for the atomic level of quantum computers. This part also concerns itself with reversible circuits as the basis for quantum circuits and specifies important issues regarding future improvements.

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