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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: 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: Sanjeev Arora
Publisher: Cambridge University Press
ISBN: 0521424267
Category : Computers
Languages : en
Pages : 609
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Book Description
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author: Richard C. Dorf
Publisher: John Wiley & Sons
ISBN: 0470521570
Category : Technology & Engineering
Languages : en
Pages : 1821
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Book Description
The central theme of Introduction to Electric Circuits is the concept that electric circuits are a part of the basic fabric of modern technology. Given this theme, this book endeavors to show how the analysis and design of electric circuits are inseparably intertwined with the ability of the engineer to design complex electronic, communication, computer and control systems as well as consumer products.This book is designed for a one-to three-term course in electric circuits or linear circuit analysis, and is structured for maximum flexibility.
Author: Rastislav Královic
Publisher: Springer Science & Business Media
ISBN: 3540377913
Category : Computers
Languages : en
Pages : 827
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Book Description
This book constitutes the refereed proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006. The book presents 62 revised full papers together with the full papers or abstracts of 7 invited talks. All current aspects in theoretical computer science and its mathematical foundations are addressed, from algorithms and data structures, to complexity, automata, semantics, logic, formal specifications, models of computation, concurrency theory, computational geometry and more.
Author: Armando Castañeda
Publisher: Springer Nature
ISBN: 303120624X
Category : Computers
Languages : en
Pages : 782
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Book Description
This book constitutes the proceedings of the 15th Latin American Symposium on Theoretical Informatics, LATIN 2022, which took place in Guanajuato, Mexico, in November 2022. The 46 papers presented in this volume were carefully reviewed and selected from 114 submissions. They were organized in topical sections as follows: Algorithms and Data Structures; Approximation Algorithms; Cryptography; Social Choice Theory; Theoretical Machine Learning; Automata Theory and Formal Languages; Combinatorics and Graph Theory; Complexity Theory; Computational Geometry. Chapter “Klee’s Measure Problem Made Oblivious” is available open access under a CC BY 4.0 license.
Author: Gábor Lugosi
Publisher: Springer Science & Business Media
ISBN: 3540352945
Category : Computers
Languages : en
Pages : 667
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Book Description
This book constitutes the refereed proceedings of the 19th Annual Conference on Learning Theory, COLT 2006, held in Pittsburgh, Pennsylvania, USA in June 2006. The 43 revised full papers presented together with 2 articles on open problems and 3 invited lectures were carefully reviewed and selected from a total of 102 submissions. The papers cover a wide range of topics including clustering, un- and semisupervised learning, statistical learning theory, regularized learning and kernel methods, query learning and teaching, inductive inference, learning algorithms and limitations on learning, online aggregation, online prediction and reinforcement learning.
