Computer Arithmetic and Formal Proofs PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Computer Arithmetic and Formal Proofs PDF full book. Access full book title Computer Arithmetic and Formal Proofs by Sylvie Boldo. Download full books in PDF and EPUB format.
Author: Sylvie Boldo
Publisher: Elsevier
ISBN: 0081011709
Category : Computers
Languages : en
Pages : 328
Get Book Here
Book Description
Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation. - Describes the notions of specification and weakest precondition computation and their practical use - Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic - Includes real analysis and a case study about numerical analysis
Author: Sylvie Boldo
Publisher: Elsevier
ISBN: 0081011709
Category : Computers
Languages : en
Pages : 328
Get Book Here
Book Description
Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation. - Describes the notions of specification and weakest precondition computation and their practical use - Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic - Includes real analysis and a case study about numerical analysis
Author: Jean-Michel Muller
Publisher: Birkhäuser
ISBN: 3319765264
Category : Mathematics
Languages : en
Pages : 640
Get Book Here
Book Description
Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers. However, making such an arithmetic reliable and portable, yet fast, is a very difficult task. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. The handbook is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.
Author: James H. Davenport
Publisher: Springer
ISBN: 3642226736
Category : Computers
Languages : en
Pages : 323
Get Book Here
Book Description
This book constitutes the joint refereed proceedings of three international events, namely the 18th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2011, the 10th International Conference on Mathematical Knowledge Management, MKM 2011, and a new track on Systems and Projects descriptions that span both the Calculemus and MKM topics, all held in Bertinoro, Italy, in July 2011. All 51 submissions passed through a rigorous review process. A total of 15 papers were submitted to Calculemus, of which 9 were accepted. Systems and Projects track 2011 there have been 12 papers selected out of 14 submissions while MKM 2011 received 22 submissions, of which 9 were accepted for presentation and publication. The events focused on the use of AI techniques within symbolic computation and the application of symbolic computation to AI problem solving; the combination of computer algebra systems and automated deduction systems; and mathematical knowledge management, respectively.
Author: Jacques Carette
Publisher: Springer Science & Business Media
ISBN: 3642026141
Category : Computers
Languages : en
Pages : 510
Get Book Here
Book Description
As computers and communications technology advance, greater opportunities arise for intelligent mathematical computation. While computer algebra, au- mated deduction and mathematical publishing each have long and successful histories, we are now seeing increasing opportunities for synergy among them. The Conferences on Intelligent Computer Mathematics (cicm 2009) is a c- lection of co-located meetings, allowing researchers and practitioners active in these related areas to share recent results and identify the next challenges. The speci?c areas of the cicm conferences and workshops are described below, but the unifying theme is the computerized handling of mathematical knowledge. The successful formalization of much of mathematics, as well as a better - derstanding of its internal structure, makes mathematical knowledge in many waysmore tractable than generalknowledge,as traditionally treatedin arti?cial intelligence. Similarly, we can also expect the problem of e?ectively using ma- ematical knowledge in automated ways to be much more tractable. This is the goal of the work in the cicm conferences and workshops. In the long view, so- ing the problems addressed by cicm is an important milestone in formulating the next generation of mathematical software.
Author: Earl E Swartzlander
Publisher: World Scientific
ISBN: 981465115X
Category : Mathematics
Languages : en
Pages : 474
Get Book Here
Book Description
Computer Arithmetic Volume III is a compilation of key papers in computer arithmetic on floating-point arithmetic and design. The intent is to show progress, evolution, and novelty in the area of floating-point arithmetic. This field has made extraordinary progress since the initial software routines on mainframe computers have evolved into hardware implementations in processors spanning a wide range of performance. Nevertheless, these papers pave the way to the understanding of modern day processors design where computer arithmetic are supported by floating-point units. The goal of Volume III is to collect the defining document for floating-point arithmetic and many of the key papers on the implementation of both binary and decimal floating-point arithmetic into a single volume. Although fewer than forty papers are included, their reference lists will direct the interested reader to other excellent work that could not be included here. Volume III is specifically oriented to the needs of designers and users of both general-purpose computers and special-purpose digital processors. The book should also be useful to systems engineers, computer architects, and logic designers. It is also intended to serve as a primary text for a course on floating-point arithmetic, as well as a supplementary text for courses in digital arithmetic and high-speed signal processing. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:OverviewFloating-Point AdditionFloating-Point MultiplicationRoundingFused Multiply AddFloating-Point DivisionElementary FunctionsDecimal Floating-Point Arithmetic Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:The papers that are included cover the key concepts needed to develop efficient (fast, small and low-power) floating-point processing unitsThe papers include presentations by the initial developers in their own words to better explain the basic techniquesIncludes five papers on decimal floating-point arithmetic, which has been added to the IEEE standardKeywords:Floating-Point Addition;Floating-Point Multiplication;Floating-Point Division;Decimal Floating-Point Arithmetic
Author: Nina Narodytska
Publisher: TU Wien Academic Press
ISBN: 3854480652
Category : Computers
Languages : en
Pages : 316
Get Book Here
Book Description
Die Proceedings zur Konferenz „Formal Methods in Computer-Aided Design 2024“ geben aktuelle Einblicke in ein spannendes Forschungsfeld. Zum fünften Mal erscheinen die Beiträge der Konferenzreihe „Formal Methods in Computer-Aided Design“ (FMCAD) als Konferenzband bei TU Wien Academic Press. Der aktuelle Band der seit 2006 jährlich veranstalteten Konferenzreihe präsentiert in 35 Beiträgen neueste wissenschaftliche Erkenntnisse aus dem Bereich des computergestützten Entwerfens. Die Beiträge behandeln formale Aspekte des computergestützten Systemdesigns einschließlich Verifikation, Spezifikation, Synthese und Test. Die FMCAD-Konferenz findet im Oktober 2024 in Prag, Tschechische Republik, statt. Sie gilt als führendes Forum im Bereich des computer-aided design und bietet seit ihrer Gründung Forschenden sowohl aus dem akademischen als auch dem industriellen Umfeld die Möglichkeit, sich auszutauschen und zu vernetzen.
Author: Florian Rabe
Publisher: Springer
ISBN: 3319968122
Category : Computers
Languages : en
Pages : 299
Get Book Here
Book Description
This book constitutes the refereed proceedings of the 11th International Conference on Intelligent Computer Mathematics, CICM 2018, held in Hagenberg, Austria, in August 2018. The 23 full papers presented were carefully reviewed and selected from a total of 36 submissions. The papers focos on the Calculemus, Digital Mathematics Libraries, and Mathematical Knowledge Management tracks which also correspond to the subject areas of the predecessor meetings. Orthogonally, the Systems and Projects track called for descriptions of digital resources, such as data and systems, and of projects, whether old, current, or new, and survey papers covering any topics of relevance to the CICM community.
Author: Omri Isac
Publisher: Springer Nature
ISBN: 3031212223
Category : Computers
Languages : en
Pages : 213
Get Book Here
Book Description
This book constitutes the refereed proceedings of the 5th International Workshop on Software Verification and Formal Methods for ML-Enables Autonomous Systems, FoMLAS 2022, and the 15th International Workshop on Numerical Software Verification, NSV 2022, which took place in Haifa, Israel, in July/August 2022. The volume contains 8 full papers from the FoMLAS 2022 workshop and 3 full papers from the NSV 2022 workshop. The FoMLAS workshop is dedicated to the development of novel formal methods techniques to discussing on how formal methods can be used to increase predictability, explainability, and accountability of ML-enabled autonomous systems. NSV 2022 is focusing on the challenges of the verification of cyber-physical systems with machine learning components.
Author: Jyotirmoy V. Deshmukh
Publisher: Springer Nature
ISBN: 3031067738
Category : Computers
Languages : en
Pages : 848
Get Book Here
Book Description
This book constitutes the proceedings of the 14th International Symposium on NASA Formal Methods, NFM 2022, held in Pasadena, USA, during May 24-27, 2022. The 33 full and 6 short papers presented in this volume were carefully reviewed and selected from 118submissions. The volume also contains 6 invited papers. The papers deal with advances in formal methods, formal methods techniques, and formal methods in practice. The focus on topics such as interactive and automated theorem proving; SMT and SAT solving; model checking; use of machine learning and probabilistic reasoning in formal methods; formal methods and graphical modeling languages such as SysML or UML; usability of formal method tools and application in industry, etc.
Author: Lubos Brim
Publisher: Springer
ISBN: 3540709525
Category : Computers
Languages : en
Pages : 372
Get Book Here
Book Description
This book constitutes the thoroughly refereed joint post-proceedings of the two International Workshops on Formal Methods for Industrial Critical Systems, FMICS 2006, and on Parallel and Distributed Methods in Verification, PDMC 2006, held in Bonn, Germany in August 2006 in the course of the 17th International Conference on Concurrency Theory, CONCUR 2006.
