From Boolean Matrix Theory To Logical Dynamical Systems
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From Boolean Matrix Theory to Logical Dynamical Systems
This book offers a systematic platform for the theory of Boolean matrix and its application in logical dynamical systems. As a special kind of non-negative matrix, Boolean matrix has wide applications in graph theory, discrete-event system, game theory, clustering analysis, and so on. Due to the special operations between Boolean matrices, there exist some special mathematical properties for Boolean polynomial and Boolean vector space, which necessitate a general theory of Boolean matrix. Furthermore, logical dynamical systems have received recent attention from systems biology, information security, artificial intelligence, etc. The development of logical dynamical systems needs the mathematical foundation of Boolean matrix and logical matrix. Therefore, it is necessary to explore the relation between Boolean matrix theory and logical dynamical systems. To our best knowledge, there are no published books available on both Boolean matrix theory and logical dynamical systems. This book aims to provide some recent insightful results to meet this gap. It can serve as a textbook for scholars and students of mathematics, cybernetics, biology and artificial intelligence. Especially, the book is an important reference for readers who are interested in Boolean matrix theory and logical dynamical systems.
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. Dimension-varying systems feature prominently across many disciplines, and through innovative applications its newly developed theory can revolutionize large data systems such as genomics and biosystems, deep learning, IT, and information-based engineering applications. - Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems. - Offers potential applications to the analysis and control of new dimension-varying systems. - Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.
Analysis and Control of Finite-Valued Systems
A comprehensive work in finite-value systems that covers the latest achievements using the semi-tensor product method, on various kinds of finite-value systems. These results occupy the highest position in the analysis and control of this field. It not only covers all aspects of research in finite-value systems, but also presents the mathematical derivation for each conclusion in depth. The book contains examples to provide a better understanding of the practical applications of finite-value systems. It will serve as a textbook for graduate students of Cybernetics, Mathematical, and Biology, and a reference for readers interested in the theory of finite-value systems.