Jeffrey Zheng Editor Variant Construction from Theoretical Foundation to Applications Variant Construction from Theoretical Foundation to Applications Jeffrey Zheng Editor Variant Construction from Theoretical Foundation to Applications 123 Editor Jeffrey Zheng School of Software Yunnan University Kunming, Yunnan, China ISBN 978-981-13-2281-5 ISBN 978-981-13-2282-2 (eBook) https://doi.org/10.1007/978-981-13-2282-2 Library of Congress Control Number: 2018958351 © The Editor(s) (if applicable) and The Author(s) 2019. This book is an open access publication. Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made. 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Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Dedicated to I-Ching—First Variant Construction Lan Z. Yin & Su M. Zheng—Mother & Father Qing S. Gao—Mentor on Parallel Sorting Algorithm & Computer Architecture Tasiyasu L. Kunii—Master on Meta Knowledge Bob Beaumont—Adviser on Optimization Ping Zhang—Wife Graduate School of USTC & UCAS—40-th Anniversary (1978–2018) Foreword Dr. Jeffrey Zheng was one of the first postgraduate students supervised by Prof. Qingshi Gao (Member, Chinese Academy of Sciences) at the Institute of Computing Technology, Chinese Academy of Sciences. I have known Dr. Zheng for 40 years since then. Building upon his postgraduate work (Parallel Sorting Algorithm and 0-1 Transformation), Dr. Zheng has made significant contribution to the field of Variant Construction, ranging from theoretical foundations to various applications. His research has been published at many academic journals and conferences. For the convenience of readers, Dr. Zheng compiled his representative works of 40 years into two monographs with complementary contents. I believe that professionals in related fields will find this book both an excellent reference and a source of inspi- ration. Other readers will enjoy this book as an introduction to topics of Variant Construction. I am very happy to recommend this book in the form of a foreword. Beijing, China Yunmei Dong April 2018 Professor, The Institute of Software Chinese Academy of Sciences Member, Chinese Academy of Sciences As head of the R&D team for Lenovo Chinese Systems, I am very pleased to see the research work of former colleague Dr. Jeffrey Zheng, which began 30 years ago with the “Smoothly Enlarging Chinese Font Algorithm of 0-1 logic operations” at the Institute of Computing Technology of the Chinese Science Academy. His most recent work “Variant Construction” is summarized as a professional monograph. I expect this new measurement system to be used efficiently for advanced crypto- graphic tests in modern cyberspace security. I am pleased to give this foreword. Beijing, China Guangnan Ni April 2018 Professor, The Institute of Computing Technology Chinese Academy of Sciences Member, Chinese Academy of Engineering vii viii Foreword Dr. Jeffrey Zheng and I were in the first group of postgraduates major in Computer Architecture at the Graduate School of the Chinese Academy of Sciences 40 years ago. Professor Qingshi Gao (Member, Chinese Academy of Sciences) supervised him in particular in the areas of parallel algorithm and computer architecture. Dr. Jeffrey Zheng is one of the few classmates who continue to works in basic research and advanced applications. It is great for Dr. Jeffrey Zheng to collect his research work in a monograph. Variant Measurement Technology could be used in the next generation of Quantum Cryptographic Communication Services. On the occasion of the 40th anniversary of the Graduate School of Chinese Academy of Sciences, I would like to express my good wishes as a classmate for this monograph in the foreword. Beijing, China Guojie Li April 2018 Professor, The Institute of Computing Technology Chinese Academy of Sciences Member, Chinese Academy of Engineering Preface Associated with the fast development of science and technology in the twenty-first century, the modern computer and communication system in optical fiber com- munication supporting the global Internet shows profound influence on society and economy. As a result, globalization has become an extremely important issue in social and economic systems. The Internet and optical fiber communication systems have revolutionized the geographic and communication patterns of the world, by creating an open era of integrated global Internet connectivity. Quantum key communication technology and quantum entanglement experiments on a quantum satellite represent typical examples of China’s world-leading science and technol- ogy from the perspective of frontier application research. The latest achievements of artificial intelligence, which is the lead of Alpha-Go, show the potential intelligence prospect of advanced technology based on deep learning, artificial neural networks, and knowledge-based support vector machine systems. Related achievements are very attractive, such as poetry robots, service robots, industrial robots, face recognition, gesture recognition, unmanned aerial vehicles, self-driving cars, and unmanned underwater vehicles. A list of military and civilian high-tech achieve- ments supports daily life with rich and colorful intelligent products. From the viewpoint of mathematics and logics, the foundation framework to design and simulate both modern computer systems and optical fiber communi- cation networks is dependent on the 0-1 logical system and representations of multiple bit states. For integrated circuits, the theoretical basis can be traced back to the 1930s. Shannon developed the Boolean algebra to design circuits establishing switch circuit theory, Turing proposed the Turing machine, and von Neumann established a modern computer architecture. After more than 50 years of devel- opment follows Moore’s Law: the observation that the number of transistors in a dense integrated circuit doubles approximately every 2 years. Optimization of very large-scale integrated circuit technology appears everywhere with evolution of magical functions. ix x Preface Looking ahead, the development of advanced science and technology is subject to the limitations of basic theory and applications on foundational supports. From the perspective of basic research, how we can extend this classical level is a very interesting issue and an extremely difficult research topic. Purpose of This Book After four decades of deep exploration on 0-1 logical systems, the authors expended vector 0-1 logical systems to establish a variant logic framework in 2010. After further research and development for one decade, three theoretical components were established: variant logic, variant measurement, and variant map. At the same time, various sample applications were investigated and developed. However, because most published papers are scattered in professional journals, conference proceedings, and academic books, it is difficult for other people to obtain com- prehensive information on the topic. In addition, each article may be focused on a specific issue, and it is difficult for readers to understand the whole structure from a few papers. We are going to organize relevant papers in this book, which will be the first book on variant construction with intrinsic logical connections on the selected papers. Selected papers are composed of different parts. Based on this architecture, different readers can easily access suitable content from specific chapters. The Need for a New Logic System In modern computer and communication systems, the theory of switch circuits uses multiple bits, states, and logic operations for state automata and combinatorial logic units to design and implement complex computing and communication systems. For solving linear equations with n variables as algebraic equation, Boolean equation or differential equation, it is useful to apply a matrix associated with a set of eigenvectors. Matrices and eigenvalues are valid to provide solutions on periodic problems of special basis