Algebraic Circuits
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Algebraic Circuits
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Author : Antonio Lloris Ruiz
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-05
Algebraic Circuits written by Antonio Lloris Ruiz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-05 with Technology & Engineering categories.
This book presents a complete and accurate study of algebraic circuits, digital circuits whose performance can be associated with any algebraic structure. The authors distinguish between basic algebraic circuits, such as Linear Feedback Shift Registers (LFSRs) and cellular automata and algebraic circuits, such as finite fields or Galois fields. The book includes a comprehensive review of representation systems, of arithmetic circuits implementing basic and more complex operations and of the residue number systems (RNS). It presents a study of basic algebraic circuits such as LFSRs and cellular automata as well as a study of circuits related to Galois fields, including two real cryptographic applications of Galois fields.
Arithmetic And Algebraic Circuits
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Author : Antonio Lloris Ruiz
language : en
Publisher: Springer Nature
Release Date : 2021-03-27
Arithmetic And Algebraic Circuits written by Antonio Lloris Ruiz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-27 with Technology & Engineering categories.
This book presents a complete and accurate study of arithmetic and algebraic circuits. The first part offers a review of all important basic concepts: it describes simple circuits for the implementation of some basic arithmetic operations; it introduces theoretical basis for residue number systems; and describes some fundamental circuits for implementing the main modular operations that will be used in the text. Moreover, the book discusses floating-point representation of real numbers and the IEEE 754 standard. The second and core part of the book offers a deep study of arithmetic circuits and specific algorithms for their implementation. It covers the CORDIC algorithm, and optimized arithmetic circuits recently developed by the authors for adders and subtractors, as well as multipliers, dividers and special functions. It describes the implementation of basic algebraic circuits, such as LFSRs and cellular automata. Finally, it offers a complete study of Galois fields, showing some exemplary applications and discussing the advantages in comparison to other methods. This dense, self-contained text provides students, researchers and engineers, with extensive knowledge on and a deep understanding of arithmetic and algebraic circuits and their implementation.
The Algebraic Theory Of Switching Circuits
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Author : Gr. C. Moisil
language : en
Publisher: Elsevier
Release Date : 2014-07-10
The Algebraic Theory Of Switching Circuits written by Gr. C. Moisil and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Technology & Engineering categories.
The Algebraic Theory of Switching Circuits covers the application of various algebraic tools to the delineation of the algebraic theory of switching circuits for automation with contacts and relays. This book is organized into five parts encompassing 31 chapters. Part I deals with the principles and application of Boolean algebra and the theory of finite fields (Galois fields). Part II emphasizes the importance of the sequential operation of the automata and the variables associated to the current and to the contacts. This part also tackles the recurrence relations that describe operations of the network and the principles of the so-called characteristic equations. Part III reviews the study of networks with secondary elements other than ordinary relays, while Part IV focuses on the fundamentals and application of multi-position contacts. Part V considers several topics related to circuit with electronic elements, including triodes, pentodes, transistors, and cryotrons. This book will be of great value to practicing engineers, mathematicians, and workers in the field of computers.
Arithmetic Circuits
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Author : Amir Shpilka
language : en
Publisher: Now Publishers Inc
Release Date : 2010
Arithmetic Circuits written by Amir Shpilka and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
A large class of problems in symbolic computation can be expressed as the task of computing some polynomials; and arithmetic circuits form the most standard model for studying the complexity of such computations. This algebraic model of computation attracted a large amount of research in the last five decades, partially due to its simplicity and elegance. Being a more structured model than Boolean circuits, one could hope that the fundamental problems of theoretical computer science, such as separating P from NP, will be easier to solve for arithmetic circuits. However, in spite of the appearing simplicity and the vast amount of mathematical tools available, no major breakthrough has been seen. In fact, all the fundamental questions are still open for this model as well. Nevertheless, there has been a lot of progress in the area and beautiful results have been found, some in the last few years. As examples we mention the connection between polynomial identity testing and lower bounds of Kabanets and Impagliazzo, the lower bounds of Raz for multilinear formulas, and two new approaches for proving lower bounds: Geometric Complexity Theory and Elusive Functions. The goal of this monograph is to survey the field of arithmetic circuit complexity, focusing mainly on what we find to be the most interesting and accessible research directions. We aim to cover the main results and techniques, with an emphasis on works from the last two decades. In particular, we discuss the recent lower bounds for multilinear circuits and formulas, the advances in the question of deterministically checking polynomial identities, and the results regarding reconstruction of arithmetic circuits. We do, however, also cover part of the classical works on arithmetic circuits. In order to keep this monograph at a reasonable length, we do not give full proofs of most theorems, but rather try to convey the main ideas behind each proof and demonstrate it, where possible, by proving some special cases.
Introduction To Circuit Complexity
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Author : Heribert Vollmer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Introduction To Circuit Complexity written by Heribert Vollmer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Computers categories.
An advanced textbook giving a broad, modern view of the computational complexity theory of boolean circuits, with extensive references, for theoretical computer scientists and mathematicians.
Basic Matrix Algebra And Transistor Circuits
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Author : G. Zelinger
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Basic Matrix Algebra And Transistor Circuits written by G. Zelinger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Technology & Engineering categories.
Basic Matrix Algebra and Transistor Circuits deals with mastering the techniques of matrix algebra for application in transistors. This book attempts to unify fundamental subjects, such as matrix algebra, four-terminal network theory, transistor equivalent circuits, and pertinent design matters. Part I of this book focuses on basic matrix algebra of four-terminal networks, with descriptions of the different systems of matrices. This part also discusses both simple and complex network configurations and their associated transmission. This discussion is followed by the alternative methods of deriving the transmission matrix using Kirchhoff's law. Part II introduces matrix analysis of transistor circuits, and then shows in detail the three transistor configurations: common-base, common-emitter, and common collector. A step-by-step method of transmission matrices derivation for each transistor configuration is then explained. This book notes the significance of matrix algebra in dealing with amplifier problems in a variety of output network configurations. Part III focuses on several aspects of single-stage transistor ampler design. This part explains how matrix algebra can be used to derive the exact input, output impedances, and the reverse transfer properties of transistor amplifiers with full load and generator terminations. Through mathematical analysis, the book shows the accuracy of matrix analysis in transistor amplifier design. This book is suitable for design engineers, electrical engineers, and students and practitioners of applied mathematics.
Computation Of The Additive Complexity Of Algebraic Circuits With Root Extracting
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Author : International Computer Science Institute
language : en
Publisher:
Release Date : 1992
Computation Of The Additive Complexity Of Algebraic Circuits With Root Extracting written by International Computer Science Institute and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computational complexity categories.
Abstract: "We design an algorithm for computing the generalized (algebraic circuits with root extraction) additive complexity of any rational function. It is the first computability result of this sort on the additive complexity of algebraic circuits (cf. [SW 80])."
Modeling Digital Switching Circuits With Linear Algebra
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Author : Mitchell A. Thornton
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Modeling Digital Switching Circuits With Linear Algebra written by Mitchell A. Thornton and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.
Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0, 1} allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of transfer functions is ubiquitous in many areas of engineering and their rich background in linear systems theory and signal processing is easily applied to digital switching circuits with this model. The common tasks of circuit simulation and justification are specific examples of the application of the linear algebraic model and are described in detail. The advantages offered by the new model as compared to traditional methods are emphasized throughout the book. Furthermore, the new approach is easily generalized to other types of information processing circuits such as those based upon multiple-valued or quantum logic; thus providing a unifying mathematical framework common to each of these areas. Modeling Digital Switching Circuits with Linear Algebra provides a blend of theoretical concepts and practical issues involved in implementing the method for circuit design tasks. Data structures are described and are shown to not require any more resources for representing the underlying matrices and vectors than those currently used in modern electronic design automation (EDA) tools based on the Boolean model. Algorithms are described that perform simulation, justification, and other common EDA tasks in an efficient manner that are competitive with conventional design tools. The linear algebraic model can be used to implement common EDA tasks directly upon a structural netlist thus avoiding the intermediate step of transforming a circuit description into a representation of a set of switching functions as is commonly the case when conventional Boolean techniques are used. Implementation results are provided that empirically demonstrate the practicality of the linear algebraic model.
Computation Of The Additive Complexity Of Algebraic Circuits With Root Extracting
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Author : Dima J. Grigorʹev
language : de
Publisher:
Release Date : 1992
Computation Of The Additive Complexity Of Algebraic Circuits With Root Extracting written by Dima J. Grigorʹev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computational complexity categories.
Abstract: "We design an algorithm for computing the generalized (algebraic circuits with root extraction) additive complexity of any rational function. It is the first computability result of this sort on the additive complexity of algebraic circuits (cf. [SW 80])."
Differential Algebraic Systems
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Author : Ricardo Riaza
language : en
Publisher: World Scientific
Release Date : 2008
Differential Algebraic Systems written by Ricardo Riaza and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Differential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory.Beginning with elementary aspects, the author succeeds in providing a self-contained and comprehensive presentation of several advanced topics in DAE theory, such as the full characterization of linear time-varying equations via projector methods or the geometric reduction of nonlinear systems. Recent results on singularities are extensively discussed. The book also addresses in detail differential-algebraic models of electrical and electronic circuits, including index characterizations and qualitative aspects of circuit dynamics. In particular, the reader will find a thorough discussion of the state/semistate dichotomy in circuit modeling. The state formulation problem, which has attracted much attention in the engineering literature, is cleverly tackled here as a reduction problem on semistate models.