Arithmetic And Algebraic Circuits
DOWNLOAD
Download Arithmetic And Algebraic Circuits PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Arithmetic And Algebraic Circuits book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Arithmetic And Algebraic Circuits
DOWNLOAD
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.
Algebraic Circuits
DOWNLOAD
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 Circuits
DOWNLOAD
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.
Formal Analysis Of Arithmetic Circuits Using Computer Algebra Verification Abstraction And Reverse Engineering
DOWNLOAD
Author : Cunxi Yu
language : en
Publisher:
Release Date : 2017
Formal Analysis Of Arithmetic Circuits Using Computer Algebra Verification Abstraction And Reverse Engineering written by Cunxi Yu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Despite a considerable progress in verification and abstraction of random and control logic, advances in formal verification of arithmetic designs have been lagging. This can be attributed mostly to the difficulty in an efficient modeling of arithmetic circuits and datapaths without resorting to computationally expensive Boolean methods, such as Binary Decision Diagrams (BDDs) and Boolean Satisfiability (SAT), that require "bit blasting", i.e., flattening the design to a bit-level netlist. Approaches that rely on computer algebra and Satisfiability Modulo Theories (SMT) methods are either too abstract to handle the bit-level nature of arithmetic designs or require solving computationally expensive decision or satisfiability problems. The work proposed in this thesis aims at overcoming the limitations of analyzing arithmetic circuits, specifically at the post-synthesized phase. It addresses the verification, abstraction and reverse engineering problems of arithmetic circuits at an algebraic level, treating an arithmetic circuit and its specification as a properly constructed algebraic system. The proposed technique solves these problems by function extraction, i.e., by deriving arithmetic function computed by the circuit from its low-level circuit implementation using computer algebraic rewriting technique. The proposed techniques work on large integer arithmetic circuits and finite field arithmetic circuits, up to 512-bit wide containing millions of logic gates.
Basic Electronics Math
DOWNLOAD
Author : Clyde Herrick
language : en
Publisher: Elsevier
Release Date : 1997-03-19
Basic Electronics Math written by Clyde Herrick and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-19 with Mathematics categories.
Most students entering an electronics technician program have an understanding of mathematics. Basic Electronics Math provides is a practical application of these basics to electronic theory and circuits. The first half of Basic Electronics Math provides a refresher of mathematical concepts. These chapters can be taught separately from or in combination with the rest of the book, as needed by the students. The second half of Basic Electronics Math covers applications to electronics. Basic concepts of electronics math Numerous problems and examples Uses real-world applications
Introduction To Circuit Complexity
DOWNLOAD
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.
Algebraic Methods In Computational Complexity
DOWNLOAD
Author : Satyanarayana V. Lokam
language : en
Publisher:
Release Date : 1996
Algebraic Methods In Computational Complexity written by Satyanarayana V. Lokam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Computational complexity categories.
Incremental Column Wise Verification Of Arithmetic Circuits Using Computer Algebra
DOWNLOAD
Author : Daniela Kaufmann
language : en
Publisher:
Release Date : 2020
Incremental Column Wise Verification Of Arithmetic Circuits Using Computer Algebra written by Daniela Kaufmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Abstract: Verifying arithmetic circuits and most prominently multiplier circuits is an important problem which in practice still requires substantial manual effort. The currently most effective approach uses polynomial reasoning over pseudo boolean polynomials. In this approach a word-level specification is reduced by a Gröbner basis which is implied by the gate-level representation of the circuit. This reduction returns zero if and only if the circuit is correct. We give a rigorous formalization of this approach including soundness and completeness arguments. Furthermore we present a novel incremental column-wise technique to verify gate-level multipliers. This approach is further improved by extracting full- and half-adder constraints in the circuit which allows to rewrite and reduce the Gröbner basis. We also present a new technical theorem which allows to rewrite local parts of the Gröbner basis. Optimizing the Gröbner basis reduces computation time substantially. In addition we extend these algebraic techniques to verify the equivalence of bit-level multipliers without using a word-level specification. Our experiments show that regular multipliers can be verified efficiently by using off-the-shelf computer algebra tools, while more complex and optimized multipliers require more sophisticated techniques. We discuss in detail our complete verification approach including all optimizations
Completeness And Reduction In Algebraic Complexity Theory
DOWNLOAD
Author : Peter Bürgisser
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Completeness And Reduction In Algebraic Complexity Theory written by Peter Bürgisser 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 2013-03-14 with Mathematics categories.
This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.
Boolean Algebra And Its Applications
DOWNLOAD
Author : J. Eldon Whitesitt
language : en
Publisher: Courier Corporation
Release Date : 2012-05-24
Boolean Algebra And Its Applications written by J. Eldon Whitesitt and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.