Logic Functions and Equations

ISBN-13: 9783030889470 / Miękka / 2023 / 810 str.

Christian Posthoff

Spis treści

Part I Theoretical Foundations

1. Basic Algebraic Structures

2. Logic Functions

3. Logic Equations

4. Boolean Differential Calculus

5. Sets, Lattices, and Classes Logic Functions

Part II Applications

6. Logics, Arithmetic, and Special Functions

7. SAT-Problems

8. Extremely Complex Problems

9. Combinational Circuits

10. Sequential Circuits

References

Index

O autorze

Bernd Steinbach studied Information Technology at the University of Technology in Chemnitz (Germany) and graduated with an M.Sc. in 1973. He graduated with a Ph.D. and with a Dr. sc. techn. (Doctor scientiae technicarum) for his second doctoral thesis from the Faculty of Electrical Engineering of the Chemnitz University of Technology in 1981 and 1984, respectively. In 1991 he obtained the Habilitation (Dr.-Ing. habil.) from the same Faculty. Topics of his theses involved Boolean equations, Boolean differential equations, and their application in the field of circuit design using efficient algorithms and data structures on computers.

He was working in industry as an Electrician, there he tested professional controlling systems at the Niles Company. After finishing his studies, he taught as Assistant Lecturer at the Department of Information Technology of the Chemnitz University of Technology. In a following period of industrial occupation as a research engineer he developed programs for test pattern generation for computer circuits at the company ROBOTRON. Thereafter he returned to the Department of Information Technology of the Chemnitz University of Technology as Associate Professor for design automation in logic design.

From 1992 to 2017 he was a Full Professor of Computer Science / Software Engineering and Programming at the Freiberg University of Mining and Technology, Department of Computer Science. He served as Head of the Department of Computer Science and Vice-Dean of the Faculty of Mathematics and Computer Science. His research areas include logic functions and equations and their application in many fields, such as Artificial Intelligence, UML - based testing of software, UML - based hardware / software co-design, and extremely complex problems. He is the head of a group that developed the XBOOLE software system. He is co-author and editor of 19 books. He published more than 280 chapters in books, complete issues of journals, and papers in journals and proceedings.

He has served as Program Chairman for the IEEE International Symposium on Multiple-Valued Logic (ISMVL), and as guest editor of the Journal of Multiple-Valued Logic and Soft Computing. He is the initiator and was the general chair of the first 12 workshops of a biennial series of International Workshops on Boolean Problems (IWSBP), which started in 1994. He received the Barkhausen Award from the University of Technology Dresden in 1983.

Christian Posthoff studied Mathematics at the University of Leipzig. From 1968 to 1972, he worked as a programmer and in the field of Operations Research; simultaneously, he did his Ph.D. in 1975 with the thesis "Application of Mathematical Methods in Communicative Psychotherapy". In 1972, he began working at the Department of Information Technology at the Chemnitz University of Technology; up to 1983, his research activities concentrated on logic design. Important results have been algorithms and programs for solving Boolean equations with a high number of variables and the Boolean Differential Calculus (a generalized differential and integral calculus for Boolean rings) for the analytical treatment of different problems in the field of logic design. These results have been collected in a monograph "Binary Dynamic Systems", and allowed the habilitation (Dr.-Ing. habil.) at the Faculty of Electrical Engineering in 1979 and the promotion to Associate Professor. In 1983, he was promoted to Full Professor of Computer Science in the Department of Computer Science at the same university, and since 1984, he was Head of the Institute of Theoretical Computer Science and Artificial Intelligence and Research Director of the Department of Computer Science. His research activities included the application of fuzzy logics for the modeling of human-like "thinking" methods, learning from examples, the construction of intelligent tutoring systems, the parallelization of inference mechanisms, systems of diagnosis and configuration. He received the Scientific Award of the Chemnitz University of Technology four times.

In 1994, he moved to the Chair of Computer Science at The University of The West Indies, St. Augustine, Trinidad & Tobago. From 1996 to 2002 he was Head of the Department of Mathematics & Computer Science. He mainly focused on the development of Computer Science education at the undergraduate and graduate levels to attain international standard. Twenty years later it can be said that these intentions were very successfully fulfilled. In 2001, he received the Vice-Chancellor's Award of Excellence.  From 2010 – 2012 he spent two years at St. Georges University in Grenada with the same goals. Since his return to Germany (now retired) he devoted his efforts to the interdisciplinary research and education in several areas (Computer Science – Mathematics – Applications in different fields). He is the author or co-author of more than 25 books and many publications in journals and conference proceedings.

Blurb

The greatly expanded and updated 3rd edition of this textbook offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science and engineering. The authors’ approach emphasizes a thorough understanding of the fundamental principles as well as numerical and computer-based solution methods. The book provides insight into applications across propositional logic, binary arithmetic, coding, cryptography, complexity, logic design, and artificial intelligence.

Updated throughout, some major additions for the 3rd edition include:

• a new chapter about the concepts contributing to the power of XBOOLE;
  
• a new chapter that introduces into the application of the XBOOLE-Monitor XBM 2;
  
• many tasks that support the readers in amplifying the learned content at the end of the chapters;
  
• solutions of a large subset of these tasks to confirm learning success;
  
• challenging tasks that need the power of the XBOOLE software for their solution.
  

The XBOOLE-monitor XBM 2 software is used to solve the exercises; in this way the time-consuming and error-prone manipulation on the bit level is moved to an ordinary PC, more realistic tasks can be solved, and the challenges of thinking about algorithms leads to a higher level of education.