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Author: Antonio Lloris Ruiz
Publisher: Springer Science & Business Media
ISBN: 3642546498
Category : Technology & Engineering
Languages : en
Pages : 413
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Book Description
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.
Author: Antonio Lloris Ruiz
Publisher: Springer Science & Business Media
ISBN: 3642546498
Category : Technology & Engineering
Languages : en
Pages : 413
Get Book Here
Book Description
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.
Author: Antonio Lloris Ruiz
Publisher: Springer Nature
ISBN: 3030672662
Category : Technology & Engineering
Languages : en
Pages : 686
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Book Description
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.
Author: Elliott Mendelson
Publisher: McGraw Hill Professional
ISBN: 9780070414600
Category : Juvenile Nonfiction
Languages : en
Pages : 226
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Book Description
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Author: Amir Shpilka
Publisher: Now Publishers Inc
ISBN: 1601984006
Category : Computers
Languages : en
Pages : 193
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Book Description
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.
Author: Lenore Blum
Publisher: Springer Science & Business Media
ISBN: 1461207010
Category : Computers
Languages : en
Pages : 456
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Book Description
The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.
Author: Lawrence P. Huelsman
Publisher: Courier Corporation
ISBN: 0486280446
Category : Technology & Engineering
Languages : en
Pages : 306
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Book Description
This high-level text explains the mathematics behind basic circuit theory. It covers matrix algebra, the basic theory of n-dimensional spaces, and applications to linear systems. Numerous problems. 1963 edition.
Author: Kristian Gjøsteen
Publisher: CRC Press
ISBN: 1000630803
Category : Computers
Languages : en
Pages : 940
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Book Description
Practical Mathematical Cryptography provides a clear and accessible introduction to practical mathematical cryptography. Cryptography, both as a science and as practice, lies at the intersection of mathematics and the science of computation, and the presentation emphasises the essential mathematical nature of the computations and arguments involved in cryptography. Cryptography is also a practical science, and the book shows how modern cryptography solves important practical problems in the real world, developing the theory and practice of cryptography from the basics to secure messaging and voting. The presentation provides a unified and consistent treatment of the most important cryptographic topics, from the initial design and analysis of basic cryptographic schemes towards applications. Features Builds from theory toward practical applications Suitable as the main text for a mathematical cryptography course Focus on secure messaging and voting systems.
Author: Vladimir P. Gerdt
Publisher: Springer
ISBN: 3319022970
Category : Computers
Languages : en
Pages : 457
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Book Description
This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.
Author: Giovanni Vigna
Publisher: Springer
ISBN: 3540686711
Category : Computers
Languages : en
Pages : 269
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Book Description
New paradigms can popularize old technologies. A new \standalone" paradigm, the electronic desktop, popularized the personal computer. A new \connected" paradigm, the web browser, popularized the Internet. Another new paradigm, the mobile agent, may further popularize the Internet by giving people greater access to it with less eort. MobileAgentParadigm The mobile agent paradigm integrates a network of computers in a novel way designed to simplify the development of network applications. To an application developer the computers appear to form an electronic world of places occupied by agents. Each agent or place in the electronic world has the authority of an individual or an organization in the physical world. The authority can be established, for example, cryptographically. A mobile agent can travel from one place to another subject to the des- nation place’s approval. The source and destination places can be in the same computer or in di erent computers. In either case,the agentinitiates the trip by executing a \go" instruction which takes as an argument the name or address of the destination place. The next instruction in the agent’s program is executed in the destination place, rather than in the source place. Thus, in a sense, the mobile agent paradigm reduces networking to a program instruction. A mobile agent can interact programmatically with the places it visits and, if the other agents approve, with the other agents it encounters in those places.
Author: Rahul Santhanam
Publisher: Springer Nature
ISBN: 3030794164
Category : Computers
Languages : en
Pages : 485
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Book Description
This book constitutes the proceedings of the 16th International Computer Science Symposium in Russia, CSR 2021, held in Sochi, Russia, in June/July 2021. The 28 full papers were carefully reviewed and selected from 68 submissions. The papers cover a broad range of topics, such as formal languages and automata theory, geometry and discrete structures; theory and algorithms for application domains and much more.
