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- Computer Arithmetic and Formal Proofs

- Author : Sylvie Boldo
- Publsiher : Elsevier
- Release : 17 November 2017
- ISBN : 0081011709
- Pages : 326 pages
- Rating : /5 from reviews

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Download or read book entitled *Computer Arithmetic and Formal Proofs* by author: *Sylvie Boldo* which was release on *17 November 2017* and published by *Elsevier* with total page 326 pages . This book available in PDF, EPUB and Kindle Format. 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,Guillaume Melquiond
- Publisher : Elsevier
- Release Date : 2017-11-17
- Total pages : 326
- ISBN : 0081011709

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**Summary :** 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 ...

- Author : Lidiya Atanassova,Jurgen Herzberger,Jürgen Herzberger
- Publisher : North Holland
- Release Date : 1992
- Total pages : 504
- ISBN : 0081011709

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**Summary :** Scientists concerned with the interaction between computer arithmetic, programming languages and scientific computing will be particularly interested in this book. It focuses on papers presented at the conference and highlights the increasing impact of SCAN-91 in this area. The volume contains original research and expository articles on the field of ...

- Author : Jean-Michel Muller,Nicolas Brunie,Florent de Dinechin,Claude-Pierre Jeannerod,Mioara Joldes,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Serge Torres
- Publisher : Birkhäuser
- Release Date : 2018-05-02
- Total pages : 627
- ISBN : 0081011709

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**Summary :** 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 ...

- Author : Earl E Swartzlander,Carl E Lemonds
- Publisher : World Scientific
- Release Date : 2015-02-12
- Total pages : 472
- ISBN : 0081011709

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**Summary :** 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 ...

- Author : Dieter Probst,Peter Schuster
- Publisher : Walter de Gruyter GmbH & Co KG
- Release Date : 2016-07-25
- Total pages : 384
- ISBN : 0081011709

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**Summary :** A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive ...

- Author : Yves Nievergelt
- Publisher : Springer
- Release Date : 2015-10-13
- Total pages : 391
- ISBN : 0081011709

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**Summary :** This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science ...

- Author : David M. Russinoff
- Publisher : Springer
- Release Date : 2018-10-13
- Total pages : 382
- ISBN : 0081011709

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**Summary :** This is the first book to focus on the problem of ensuring the correctness of floating-point hardware designs through mathematical methods. Formal Verification of Floating-Point Hardware Design advances a verification methodology based on a unified theory of register-transfer logic and floating-point arithmetic that has been developed and applied to the ...

- Author : Donald A. MacKenzie
- Publisher : MIT Press
- Release Date : 1998
- Total pages : 338
- ISBN : 0081011709

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**Summary :** The essays are tied together by their explorations of connections (primarily among technology, society, and knowledge) and by their general focus on modern "high" technology. They also share an emphasis on the complexity of technological formation and fixation and on the role of belief (especially self-validating belief) in technological change....

- Author : Lubos Brim,Boudewijn Haverkort,Martin Leucker,Jaco van de Pol
- Publisher : Springer
- Release Date : 2007-06-27
- Total pages : 366
- ISBN : 0081011709

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**Summary :** 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....

- Author : James H. Davenport,William M. Farmer,Florian Rabe,Josef Urban
- Publisher : Springer
- Release Date : 2011-07-18
- Total pages : 312
- ISBN : 0081011709

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**Summary :** 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 ...

- Author : Florian Rabe,William M. Farmer,Grant O. Passmore,Abdou Youssef
- Publisher : Springer
- Release Date : 2018-08-02
- Total pages : 287
- ISBN : 0081011709

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**Summary :** 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 ...

- Author : Edgar W. Kaucher
- Publisher : Unknown
- Release Date : 1991
- Total pages : 498
- ISBN : 0081011709

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**Summary :** Read online Computer Arithmetic Scientific Computation and Mathematical Modelling written by Edgar W. Kaucher, published by which was released on 1991. Download full Computer Arithmetic Scientific Computation and Mathematical Modelling Books now! Available in PDF, ePub and Kindle....

- Author : Helmut Schwichtenberg,Katharina Spies
- Publisher : IOS Press
- Release Date : 2006-01-01
- Total pages : 445
- ISBN : 0081011709

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**Summary :** "Proof technology will become an established field in software engineering. It generally aims at integrating proof processing into industrial design and verifications tools. The origins of this technology lie in the systematic understanding of a fully-fledged, precise notion of proof by mathematics and logics. Using this profound understanding, computer scientists ...

- Author : Siani L. Baker,Alan Smaill,University of Edinburgh. Department of Artificial Intelligence
- Publisher : Unknown
- Release Date : 1993
- Total pages : 13
- ISBN : 0081011709

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**Summary :** Abstract: "An important technique for investigating derivability in formal systems of arithmetic has been to embed such systems into semi- formal systems with the [omega]-rule. This paper exploits this notion within the domain of automated theorem-proving and discusses the implementation of such a proof environment, namely the CORE system ...

- Author : Russell Steven Shawn O'Connor
- Publisher : Unknown
- Release Date : 2009
- Total pages : 151
- ISBN : 0081011709

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**Summary :** Read online Incompleteness Completeness written by Russell Steven Shawn O'Connor, published by which was released on 2009. Download full Incompleteness Completeness Books now! Available in PDF, ePub and Kindle....