Incremental Column Wise Verification Of Arithmetic Circuits Using Computer Algebra
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Incremental Column Wise Verification Of Arithmetic Circuits Using Computer Algebra
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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
Formal Verification Of Structurally Complex Multipliers
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Author : Alireza Mahzoon
language : en
Publisher: Springer Nature
Release Date : 2023-02-14
Formal Verification Of Structurally Complex Multipliers written by Alireza Mahzoon and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-14 with Technology & Engineering categories.
This book addresses the challenging tasks of verifying and debugging structurally complex multipliers. In the area of verification, the authors first investigate the challenges of Symbolic Computer Algebra (SCA)-based verification, when it comes to proving the correctness of multipliers. They then describe three techniques to improve and extend SCA: vanishing monomials removal, reverse engineering, and dynamic backward rewriting. This enables readers to verify a wide variety of multipliers, including highly complex and optimized industrial benchmarks. The authors also describe a complete debugging flow, including bug localization and fixing, to find the location of bugs in structurally complex multipliers and make corrections.
Computer Aided Verification
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Author : Shuvendu K. Lahiri
language : en
Publisher: Springer Nature
Release Date : 2020-07-15
Computer Aided Verification written by Shuvendu K. Lahiri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-15 with Computers categories.
The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic.
Tools And Algorithms For The Construction And Analysis Of Systems
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Author : Jan Friso Groote
language : en
Publisher: Springer Nature
Release Date : 2021-03-22
Tools And Algorithms For The Construction And Analysis Of Systems written by Jan Friso Groote and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-22 with Computers categories.
This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers.
Recent Findings In Boolean Techniques
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Author : Rolf Drechsler
language : en
Publisher: Springer Nature
Release Date : 2021-04-29
Recent Findings In Boolean Techniques written by Rolf Drechsler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-29 with Technology & Engineering categories.
This book describes recent findings in the domain of Boolean logic and Boolean algebra, covering application domains in circuit and system design, but also basic research in mathematics and theoretical computer science. Content includes invited chapters and a selection of the best papers presented at the 14th annual International Workshop on Boolean Problems.
Handbook Of Satisfiability
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Author : A. Biere
language : en
Publisher: IOS Press
Release Date : 2021-05-05
Handbook Of Satisfiability written by A. Biere and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-05 with Computers categories.
Propositional logic has been recognized throughout the centuries as one of the cornerstones of reasoning in philosophy and mathematics. Over time, its formalization into Boolean algebra was accompanied by the recognition that a wide range of combinatorial problems can be expressed as propositional satisfiability (SAT) problems. Because of this dual role, SAT developed into a mature, multi-faceted scientific discipline, and from the earliest days of computing a search was underway to discover how to solve SAT problems in an automated fashion. This book, the Handbook of Satisfiability, is the second, updated and revised edition of the book first published in 2009 under the same name. The handbook aims to capture the full breadth and depth of SAT and to bring together significant progress and advances in automated solving. Topics covered span practical and theoretical research on SAT and its applications and include search algorithms, heuristics, analysis of algorithms, hard instances, randomized formulae, problem encodings, industrial applications, solvers, simplifiers, tools, case studies and empirical results. SAT is interpreted in a broad sense, so as well as propositional satisfiability, there are chapters covering the domain of quantified Boolean formulae (QBF), constraints programming techniques (CSP) for word-level problems and their propositional encoding, and satisfiability modulo theories (SMT). An extensive bibliography completes each chapter. This second edition of the handbook will be of interest to researchers, graduate students, final-year undergraduates, and practitioners using or contributing to SAT, and will provide both an inspiration and a rich resource for their work. Edmund Clarke, 2007 ACM Turing Award Recipient: "SAT solving is a key technology for 21st century computer science." Donald Knuth, 1974 ACM Turing Award Recipient: "SAT is evidently a killer app, because it is key to the solution of so many other problems." Stephen Cook, 1982 ACM Turing Award Recipient: "The SAT problem is at the core of arguably the most fundamental question in computer science: What makes a problem hard?"
Formal Analysis Of Arithmetic Circuits Using Computer Algebra Verification Abstraction And Reverse Engineering
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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.
Improving Amulet2 For Verifying Multiplier Circuits Using Sat Solving And Computer Algebra
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Author : Daniela Kaufmann
language : en
Publisher:
Release Date : 2023
Improving Amulet2 For Verifying Multiplier Circuits Using Sat Solving And 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 2023 with categories.
Abstract: Verifying arithmetic circuits and most prominently multiplier circuits is an important problem which in practice is still considered to be challenging. One of the currently most successful verification techniques relies on algebraic reasoning. In this article, we present AMULET2, a fully automatic tool for verification of integer multipliers combining SAT solving and computer algebra. Our tool models multipliers given as and-inverter graphs as a set of polynomials and applies preprocessing techniques based on elimination theory of Gröbner bases. Finally, it uses a polynomial reduction algorithm to verify the correctness of the given circuit. AMULET2 is a re-factorization and improved re-implementation of our previous verification tool AMULET1 and cannot only be used as a stand-alone tool but also serves as a polynomial reasoning framework. We present a novel XOR-based slicing approach and discuss improvements on the data structures including monomial sharing
Fundamental Problems Of Algorithmic Algebra
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Author : Chee-Keng Yap
language : en
Publisher: Oxford University Press on Demand
Release Date : 2000
Fundamental Problems Of Algorithmic Algebra written by Chee-Keng Yap and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computers categories.
Popular computer algebra systems such as Maple, Macsyma, Mathematica, and REDUCE are now basic tools on most computers. Efficient algorithms for various algebraic operations underlie all these systems. Computer algebra, or algorithmic algebra, studies these algorithms and their properties and represents a rich intersection of theoretical computer science with classical mathematics. Fundamental Problems of Algorithmic Algebra provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives. Topics covered include the GCD, subresultants, modular techniques, the fundamental theorem of algebra, roots of polynomials, Sturm theory, Gaussian lattice reduction, lattices and polynomial factorization, linear systems, elimination theory, Grobner bases, and more. Features · Presents algorithmic ideas in pseudo-code based on mathematical concepts and can be used with any computer mathematics system · Emphasizes the algorithmic aspects of problems without sacrificing mathematical rigor · Aims to be self-contained in its mathematical development · Ideal for a first course in algorithmic or computer algebra for advanced undergraduates or beginning graduate students
Algebra Geometry And Software Systems
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Author : Michael Joswig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Algebra Geometry And Software Systems written by Michael Joswig 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.
A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.