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### Boolean Differential Calculus - a Compact Introduction and Selected Applications

Datum: 05.09.2017
Uhrzeit: 09.00 Uhr s.t.

Ort: MZH 4380

Vortragende(r): Prof. Dr. Bernd Steinbach (Freiberg University of Mining and Technology, Institute of Computer Science)

Abstract:
The Boolean Differential Calculus (BDC) is a very powerful theory that extends the basic concepts of Boolean Algebras significantly.
Its applications are based on Boolean spaces, Boolean operations, and basic structures such as Boolean Algebras and Boolean Rings, Boolean functions, Boolean equations, Boolean inequalities, incompletely specified Boolean functions, and Boolean lattices of Boolean functions. These basics, sometimes also called switching theory, are widely used in many modern information processing applications.
The BDC extends the known concepts and allows the consideration of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. The BDC defines a small number of derivative and differential operations. Many existing theorems are very welcome and allow new insights due to possible transformations of problems. The available operations of the BDC have been efficiently implemented in several software packages. The common use of the basic concepts and the BDC opens a very wide field of applications.
The roots of the BDC go back to the practical problem of testing digital circuits. The BDC deals with changes of signals which are very important in applications of the analysis and the synthesis of digital circuits. The comprehensive evaluation and utilization of properties of Boolean functions allow, for instance, to decompose Boolean functions very efficiently; this can be applied not only in circuit design, but also in data mining. Other examples for the use of the BDC are the detection of hazards or cryptography. The knowledge of the BDC gives the scientists and engineers an extended insight into Boolean problems leading to new applications, e.g., the use of Boolean lattices of Boolean functions.
This presentation gives a compact introduction into the BDC for Boolean functions and lattices. The use of the XBOOLE-Monitor as well as the XBOOLE-Library for efficient computations of operations of the BDC will be demonstrated. Selected applications show the usefulness of this calculus and should encourage the audience to find improved solutions for their problems using the Boolean Differential Calculus.

Short CV:
Bernd Steinbach studied Information Technology at the University of Technology in Chemnitz, Germany, where he graduated with an MSc in 1973, a PhD in 1981, and with a Dr. sc. techn. (Doctor scientiae technicarum) in 1984 for his second doctoral thesis from the Faculty of Electrical Engineering. In 1991, he obtained the Habilitation (Dr.-Ing. habil.) from the same Faculty. Following this, he worked as a research engineer, developing programs for test pattern generation for computer circuits at the company Robotron. He returned to the Department of Information Technology of the Chemnitz University of Technology as Associate Professor for Design Automation in Logic Design. He is currently, and has been for more than two decades, the head of a group that developed the XBOOLE software system and the head of the Steinbeis Transfer Center of Logic Systems in Chemnitz. He has been a Full Professor of Computer Science/Software Engineering and Programming at the Freiberg University of Mining and Technology since 1992. Professor Steinbach is also the co-author and editor of ten books, and has published more than 250 papers in books, journals and proceedings. He is the initiator and has been served as general chair of a biennial series of International Workshops on Boolean Problems (IWSBP), which started in 1994.