On Some Computer Aided Proofs In Analysis

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Computer Aided Proofs in Analysis

Author : Kenneth R. Meyer
Publisher : Springer Science & Business Media
ISBN 13 : 1461390923
Total Pages : 264 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Computer Aided Proofs in Analysis by : Kenneth R. Meyer

Download or read book Computer Aided Proofs in Analysis written by Kenneth R. Meyer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications COMPUTER AIDED PROOFS IN ANALYSIS is based on the proceedings of an IMA Participating Institutions (PI) Conference held at the University of Cincinnati in April 1989. Each year the 19 Participating Institutions select, through a competitive process, several conferences proposals from the PIs, for partial funding. This conference brought together leading figures in a number of fields who were interested in finding exact answers to problems in analysis through computer methods. We thank Kenneth Meyer and Dieter Schmidt for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Since the dawn of the computer revolution the vast majority of scientific compu tation has dealt with finding approximate solutions of equations. However, during this time there has been a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, number theory and combina torics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools.

Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations

Author : Mitsuhiro T. Nakao
Publisher : Springer Nature
ISBN 13 : 9811376697
Total Pages : 469 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by : Mitsuhiro T. Nakao

Download or read book Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations written by Mitsuhiro T. Nakao and published by Springer Nature. This book was released on 2019-11-11 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.

Computer-Aided Reasoning

Author : Matt Kaufmann
Publisher : Springer
ISBN 13 : 9780792378495
Total Pages : 337 pages
Book Rating : 4.3/5 (784 download)

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Book Synopsis Computer-Aided Reasoning by : Matt Kaufmann

Download or read book Computer-Aided Reasoning written by Matt Kaufmann and published by Springer. This book was released on 2000-06-30 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer-Aided Reasoning: ACL2 Case Studies illustrates how the computer-aided reasoning system ACL2 can be used in productive and innovative ways to design, build, and maintain hardware and software systems. Included here are technical papers written by twenty-one contributors that report on self-contained case studies, some of which are sanitized industrial projects. The papers deal with a wide variety of ideas, including floating-point arithmetic, microprocessor simulation, model checking, symbolic trajectory evaluation, compilation, proof checking, real analysis, and several others. Computer-Aided Reasoning: ACL2 Case Studies is meant for two audiences: those looking for innovative ways to design, build, and maintain hardware and software systems faster and more reliably, and those wishing to learn how to do this. The former audience includes project managers and students in survey-oriented courses. The latter audience includes students and professionals pursuing rigorous approaches to hardware and software engineering or formal methods. Computer-Aided Reasoning: ACL2 Case Studies can be used in graduate and upper-division undergraduate courses on Software Engineering, Formal Methods, Hardware Design, Theory of Computation, Artificial Intelligence, and Automated Reasoning. The book is divided into two parts. Part I begins with a discussion of the effort involved in using ACL2. It also contains a brief introduction to the ACL2 logic and its mechanization, which is intended to give the reader sufficient background to read the case studies. A more thorough, textbook introduction to ACL2 may be found in the companion book, Computer-Aided Reasoning: An Approach. The heart of the book is Part II, where the case studies are presented. The case studies contain exercises whose solutions are on the Web. In addition, the complete ACL2 scripts necessary to formalize the models and prove all the properties discussed are on the Web. For example, when we say that one of the case studies formalizes a floating-point multiplier and proves it correct, we mean that not only can you read an English description of the model and how it was proved correct, but you can obtain the entire formal content of the project and replay the proofs, if you wish, with your copy of ACL2. ACL2 may be obtained from its home page. The results reported in each case study, as ACL2 input scripts, as well as exercise solutions for both books, are available from this page.

Computer Aided Proofs in Analysis

Author : Kenneth R Meyer
Publisher :
ISBN 13 : 9781461390930
Total Pages : 272 pages
Book Rating : 4.3/5 (99 download)

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Book Synopsis Computer Aided Proofs in Analysis by : Kenneth R Meyer

Download or read book Computer Aided Proofs in Analysis written by Kenneth R Meyer and published by . This book was released on 1990-12-05 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Finite Precision Computations

Author : Francoise Chaitin-Chatelin
Publisher : SIAM
ISBN 13 : 0898713587
Total Pages : 244 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Lectures on Finite Precision Computations by : Francoise Chaitin-Chatelin

Download or read book Lectures on Finite Precision Computations written by Francoise Chaitin-Chatelin and published by SIAM. This book was released on 1996-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Accuracy and Reliability in Scientific Computing

Author : Bo Einarsson
Publisher : SIAM
ISBN 13 : 0898715849
Total Pages : 348 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Accuracy and Reliability in Scientific Computing by : Bo Einarsson

Download or read book Accuracy and Reliability in Scientific Computing written by Bo Einarsson and published by SIAM. This book was released on 2005-08-01 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates some of the difficulties related to scientific computing, describing how these can be overcome.

The Princeton Companion to Applied Mathematics

Author : Nicholas J. Higham
Publisher : Princeton University Press
ISBN 13 : 1400874475
Total Pages : 1031 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Princeton Companion to Applied Mathematics by : Nicholas J. Higham

Download or read book The Princeton Companion to Applied Mathematics written by Nicholas J. Higham and published by Princeton University Press. This book was released on 2015-09-15 with total page 1031 pages. Available in PDF, EPUB and Kindle. Book excerpt: The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Computer Arithmetic and Formal Proofs

Author : Sylvie Boldo
Publisher : Elsevier
ISBN 13 : 0081011709
Total Pages : 328 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Computer Arithmetic and Formal Proofs by : Sylvie Boldo

Download or read book Computer Arithmetic and Formal Proofs written by Sylvie Boldo and published by Elsevier. This book was released on 2017-11-17 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Fundamental Proof Methods in Computer Science

Author : Konstantine Arkoudas
Publisher : MIT Press
ISBN 13 : 0262342502
Total Pages : 1223 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Fundamental Proof Methods in Computer Science by : Konstantine Arkoudas

Download or read book Fundamental Proof Methods in Computer Science written by Konstantine Arkoudas and published by MIT Press. This book was released on 2017-04-28 with total page 1223 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook that teaches students to read and write proofs using Athena. Proof is the primary vehicle for knowledge generation in mathematics. In computer science, proof has found an additional use: verifying that a particular system (or component, or algorithm) has certain desirable properties. This book teaches students how to read and write proofs using Athena, a freely downloadable computer language. Athena proofs are machine-checkable and written in an intuitive natural-deduction style. The book contains more than 300 exercises, most with full solutions. By putting proofs into practice, it demonstrates the fundamental role of logic and proof in computer science as no other existing text does. Guided by examples and exercises, students are quickly immersed in the most useful high-level proof methods, including equational reasoning, several forms of induction, case analysis, proof by contradiction, and abstraction/specialization. The book includes auxiliary material on SAT and SMT solving, automated theorem proving, and logic programming. The book can be used by upper undergraduate or graduate computer science students with a basic level of programming and mathematical experience. Professional programmers, practitioners of formal methods, and researchers in logic-related branches of computer science will find it a valuable reference.

Interactive Theorem Proving

Author : Jeremy Avigad
Publisher : Springer
ISBN 13 : 3319948210
Total Pages : 657 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Interactive Theorem Proving by : Jeremy Avigad

Download or read book Interactive Theorem Proving written by Jeremy Avigad and published by Springer. This book was released on 2018-07-03 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th International Conference on Interactive Theorem Proving, ITP 2018, held in Oxford, UK, in July 2018. The 32 full papers and 5 short papers presented were carefully reviewed and selected from 65 submissions. The papers feature research in the area of logical frameworks and interactive proof assistants. The topics include theoretical foundations and implementation aspects of the technology, as well as applications to verifying hardware and software systems to ensure their safety and security, and applications to the formal verication of mathematical results. Chapters 2, 10, 26, 29, 30 and 37 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

PROCEEDINGS OF THE 21ST CONFERENCE ON FORMAL METHODS IN COMPUTER-AIDED DESIGN – FMCAD 2021

Author : Michael W. Whalen
Publisher : TU Wien Academic Press
ISBN 13 : 3854480466
Total Pages : 297 pages
Book Rating : 4.8/5 (544 download)

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Book Synopsis PROCEEDINGS OF THE 21ST CONFERENCE ON FORMAL METHODS IN COMPUTER-AIDED DESIGN – FMCAD 2021 by : Michael W. Whalen

Download or read book PROCEEDINGS OF THE 21ST CONFERENCE ON FORMAL METHODS IN COMPUTER-AIDED DESIGN – FMCAD 2021 written by Michael W. Whalen and published by TU Wien Academic Press. This book was released on 2021-10-14 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our life is dominated by hardware: a USB stick, the processor in our laptops or the SIM card in our smart phone. But who or what makes sure that these systems work stably, safely and securely from the word go? The computer - with a little help from humans. The overall name for this is CAD (computer-aided design), and it’s become hard to imagine our modern industrial world without it. So how can we be sure that the hardware and computer systems we use are reliable? By using formal methods: these are techniques and tools to calculate whether a system description is in itself consistent or whether requirements have been developed and implemented correctly. Or to put it another way: they can be used to check the safety and security of hardware and software. Just how this works in real life was also of interest at the annual conference on "Formal Methods in Computer-Aided Design (FMCAD)". Under the direction of Ruzica Piskac and Michael Whalen, the 21st Conference in October 2021 addressed the results of the latest research in the field of formal methods. A volume of conference proceedings with over 30 articles covering a wide range of formal methods has now been published for this online conference: starting from the verification of hardware, parallel and distributed systems as well as neuronal networks, right through to machine learning and decision-making procedures. This volume provides a fascinating insight into revolutionary methods, technologies, theoretical results and tools for formal logic in computer systems and system developments.

In the Realm of Organisation

Author : Robert Chia
Publisher : Routledge
ISBN 13 : 1134799160
Total Pages : 271 pages
Book Rating : 4.1/5 (347 download)

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Book Synopsis In the Realm of Organisation by : Robert Chia

Download or read book In the Realm of Organisation written by Robert Chia and published by Routledge. This book was released on 2003-05-20 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book breaks new ground, departing from an emphasis on 'organisations' as social objects and moving towards a position of analysis which situates itself in the wider context of the late modernity. The contributors of this book acknowledge the impact of Robert Cooper on their own work and develop further his insistence that organisational analysis must be understood in terms of the rationalization of society as a whole.

Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures

Author : George Deodatis
Publisher : CRC Press
ISBN 13 : 1315884887
Total Pages : 1112 pages
Book Rating : 4.3/5 (158 download)

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Book Synopsis Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures by : George Deodatis

Download or read book Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures written by George Deodatis and published by CRC Press. This book was released on 2014-02-10 with total page 1112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures contains the plenary lectures and papers presented at the 11th International Conference on STRUCTURAL SAFETY AND RELIABILITY (ICOSSAR2013, New York, NY, USA, 16-20 June 2013), and covers major aspects of safety, reliability, risk and life-cycle performance of str

Public-Key Cryptography -- PKC 2015

Author : Jonathan Katz
Publisher : Springer
ISBN 13 : 3662464470
Total Pages : 820 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Public-Key Cryptography -- PKC 2015 by : Jonathan Katz

Download or read book Public-Key Cryptography -- PKC 2015 written by Jonathan Katz and published by Springer. This book was released on 2015-03-16 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 18th International Conference on Practice and Theory in Public-Key Cryptography, PKC 2015, held in Gaithersburg, MD, USA, in March/April 2015. The 36 papers presented in this volume were carefully reviewed and selected from 118 submissions. They are organized in topical sections named: public-key encryption; e-cash; cryptanalysis; digital signatures; password-based authentication; pairint-based cryptography; efficient constructions; cryptography with imperfect keys; interactive proofs; lattice-based cryptography; and identity-based, predicate, and functional encryption.

Advances in Cryptology – ASIACRYPT 2018

Author : Thomas Peyrin
Publisher : Springer
ISBN 13 : 3030033325
Total Pages : 563 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Advances in Cryptology – ASIACRYPT 2018 by : Thomas Peyrin

Download or read book Advances in Cryptology – ASIACRYPT 2018 written by Thomas Peyrin and published by Springer. This book was released on 2018-11-22 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume set of LNCS 11272, 11273, and 11274 constitutes the refereed proceedings of the 24th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2018, held in Brisbane, Australia, in December 2018. The 65 revised full papers were carefully selected from 234 submissions. They are organized in topical sections on Post-Quantum Cryptanalysis; Encrypted Storage; Symmetric-Key Constructions; Lattice Cryptography; Quantum Symmetric Cryptanalysis; Zero-Knowledge; Public Key and Identity-Based Encryption; Side-Channels; Signatures; Leakage-Resilient Cryptography; Functional/Inner Product/Predicate Encryption; Multi-party Computation; ORQM; Real World Protocols; Secret Sharing; Isogeny Cryptography; and Foundations.

Computer Aided Verification

Author : Alexandra Silva
Publisher : Springer Nature
ISBN 13 : 3030816885
Total Pages : 940 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Computer Aided Verification by : Alexandra Silva

Download or read book Computer Aided Verification written by Alexandra Silva and published by Springer Nature. This book was released on 2021-07-16 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access two-volume set LNCS 12759 and 12760 constitutes the refereed proceedings of the 33rd International Conference on Computer Aided Verification, CAV 2021, held virtually in July 2021. The 63 full papers presented together with 16 tool papers and 5 invited papers were carefully reviewed and selected from 290 submissions. The papers were organized in the following topical sections: Part I: invited papers; AI verification; concurrency and blockchain; hybrid and cyber-physical systems; security; and synthesis. Part II: complexity and termination; decision procedures and solvers; hardware and model checking; logical foundations; and software verification.

PROCEEDINGS OF THE 22ND CONFERENCE ON FORMAL METHODS IN COMPUTER-AIDED DESIGN – FMCAD 2022

Author : Alberto Griggio
Publisher : TU Wien Academic Press
ISBN 13 : 3854480539
Total Pages : 405 pages
Book Rating : 4.8/5 (544 download)

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Book Synopsis PROCEEDINGS OF THE 22ND CONFERENCE ON FORMAL METHODS IN COMPUTER-AIDED DESIGN – FMCAD 2022 by : Alberto Griggio

Download or read book PROCEEDINGS OF THE 22ND CONFERENCE ON FORMAL METHODS IN COMPUTER-AIDED DESIGN – FMCAD 2022 written by Alberto Griggio and published by TU Wien Academic Press. This book was released on 2022-10-12 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system testing.