Logic networks and automata are facets of digital systems. The change of the design of logic networks from skills and art into a scientific discipline was possible by the development of the underlying mathematical theory called the Switching Theory. The fundamentals of this theory come from the attempts towards an algebraic description of laws of thoughts presented in the works by George J. Boole and the works on logic by Augustus De Morgan. As often the case in engineering, when the importance of a problem and the need for solving it reach certain limits, the solutions are searched by many scholars in different parts of the word, simultaneously or at about the same time, however, quite independently and often unaware of the work by other scholars. The formulation and rise of Switching Theory is such an example. This book presents a brief account of the developments of Switching Theory and highlights some less known facts in the history of it. The readers will find the book a fresh look into the development of the field revealing how difficult it has been to arrive at many of the concepts that we now consider obvious . Researchers in the history or philosophy of computing will find this book a valuable source of information that complements the standard presentations of the topic.

Universal codes efficiently compress sequences generated by stationary and ergodic sources with unknown statistics, and they were originally designed for lossless data compression. In the meantime, it was realized that they can be used for solving important problems of prediction and statistical analysis of time series, and this book describes recent results in this area. The first chapter introduces and describes the application of universal codes to prediction and the statistical analysis of time series; the second chapter describes applications of selected statistical methods to cryptography, including attacks on block ciphers; and the third chapter describes a homogeneity test used to determine authorship of literary texts. The book will be useful for researchers and advanced students in information theory, mathematical statistics, time-series analysis, and cryptography. It is assumed that the reader has some grounding in statistics and in information theory.

Fundamentals of Switching Theory and Logic Design discusses the basics of switching theory and logic design from a slightly alternative point of view and also presents links between switching theory and related areas of signal processing and system theory. Switching theory is a branch of applied mathematic providing mathematical foundations for logic design, which can be considered as a part of digital system design concerning realizations of systems whose inputs and outputs are described by logic functions.

Mathematical Nonlinear Image Processing deals with a fast growing research area. The development of the subject springs from two factors: (1) the great expansion of nonlinear methods applied to problems in imaging and vision, and (2) the degree to which nonlinear approaches are both using and fostering new developments in diverse areas of mathematics. Mathematical Nonlinear Image Processing will be of interest to people working in the areas of applied mathematics as well as researchers in computer vision. Mathematical Nonlinear Image Processing is an edited volume of original research. It has also been published as a special issue of the Journal of Mathematical Imaging and Vision. (Volume 2, Issue 2/3).

Fundamentals of Nonlinear Digital Filtering is the first book of its kind, presenting and evaluating current methods and applications in nonlinear digital filtering. Written for professors, researchers, and application engineers, as well as for serious students of signal processing, this is the only book available that functions as both a reference handbook and a textbook. Solid introductory material, balanced coverage of theoretical and practical aspects, and dozens of examples provide you with a self-contained, comprehensive information source on nonlinear filtering and its applications.

Universal codes efficiently compress sequences generated by stationary and ergodic sources with unknown statistics, and they were originally designed for lossless data compression. In the meantime, it was realized that they can be used for solving important problems of prediction and statistical analysis of time series, and this book describes recent results in this area. The first chapter introduces and describes the application of universal codes to prediction and the statistical analysis of time series; the second chapter describes applications of selected statistical methods to cryptography, including attacks on block ciphers; and the third chapter describes a homogeneity test used to determine authorship of literary texts. The book will be useful for researchers and advanced students in information theory, mathematical statistics, time-series analysis, and cryptography. It is assumed that the reader has some grounding in statistics and in information theory.

Mathematical Nonlinear Image Processing deals with a fast growing research area. The development of the subject springs from two factors: (1) the great expansion of nonlinear methods applied to problems in imaging and vision, and (2) the degree to which nonlinear approaches are both using and fostering new developments in diverse areas of mathematics. Mathematical Nonlinear Image Processing will be of interest to people working in the areas of applied mathematics as well as researchers in computer vision. Mathematical Nonlinear Image Processing is an edited volume of original research. It has also been published as a special issue of the Journal of Mathematical Imaging and Vision. (Volume 2, Issue 2/3).

Compared to binary switching functions, the multiple-valued functions (MV) offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible. Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools. This book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts (various related decision diagrams). Three-valued, or ternary functions, are traditionally used as the first extension from the binary case. They have a good feature that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favourable for ternary functions. Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other $p$-valued functions. Therefore, this book is written using a hands-on approach such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and the interconnections among them. Table of Contents: Multiple-Valued Logic Functions / Functional Expressions for Multiple-Valued Functions / Spectral Representations of Multiple-Valued Functions / Decision Diagrams for Multiple-Valued Functions / Fast Calculation Algorithms

Switching theory and logic design provide mathematical foundations and tools for digital system design that is an essential part in the research and development in almost all areas of modern technology. The vast complexity of modern digital systems implies that they can only be handled by computer aided design tools that are built on sophisticated mathematical models. Fundamentals of Switching Theory and Logic Design is aimed at providing an accessible introduction to these mathematical techniques that underlie the design tools and that are necessary for understanding their capabilities and limitations.

As is typical to many disciplines a high level of abstraction enables a unified treatment of many methodologies and techniques as well as provides a deep understanding of the subject in general. The drawback is that without a hands-on touch on the details it is difficult to develop an intuitive understanding of the techniques. We try to combine these views by providing hands-on examples on the techniques while binding these to the more general theory that is developed in parallel. For instance, the use of vector spaces and group theory unifies the spectral (Fourier-like) interpretation of polynomial, and graphic (decision diagrams) representations of logic functions, as well as provides new methods for optimization of logic functions.

Consequently, Fundamentals of Switching Theory and Logic Design discusses the fundamentals of switching theory and logic design from a slightly alternative point of view and also presents links between switching theory and related areas of signal processing and system theory. It also covers the core topics recommended in IEEE/ACM curricula for teaching and study in this area. Further, it contains several elective sections discussing topics for further research work in this area

Fundamentals of Nonlinear Digital Filtering is the first book of its kind, presenting and evaluating current methods and applications in nonlinear digital filtering. Written for professors, researchers, and application engineers, as well as for serious students of signal processing, this is the only book available that functions as both a reference handbook and a textbook. Solid introductory material, balanced coverage of theoretical and practical aspects, and dozens of examples provide you with a self-contained, comprehensive information source on nonlinear filtering and its applications.