Handbook Of Computability And Complexity In Analysis

Author : Vasco Brattka,Peter Hertling
Publisher : Springer Nature
Page : 427 pages
File Size : 40,5 Mb
Release : 2021-06-04
Category : Computers
ISBN : 9783030592349

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Handbook of Computability and Complexity in Analysis by Vasco Brattka,Peter Hertling Pdf

Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.

Author : Klaus Weihrauch
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 47,6 Mb
Release : 2000-09-14
Category : Computers
ISBN : 3540668179

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Computable Analysis by Klaus Weihrauch Pdf

Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid fundament for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.

Author : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 42,5 Mb
Release : 2009-04-20
Category : Computers
ISBN : 9780521424264

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Computational Complexity by Sanjeev Arora,Boaz Barak Pdf

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Author : International Conference on Computability and Complexity in Analysis
Publisher : Unknown
Page : 212 pages
File Size : 52,6 Mb
Release : 2006
Category : Electronic
ISBN : OCLC:898622279

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Computability and Complexity in Analysis by International Conference on Computability and Complexity in Analysis Pdf

Author : Klaus Weihrauch
Publisher : Springer
Page : 288 pages
File Size : 49,6 Mb
Release : 2013-11-20
Category : Computers
ISBN : 3642631029

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Computable Analysis by Klaus Weihrauch Pdf

Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid fundament for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.

Author : Robert I. Soare
Publisher : Springer
Page : 263 pages
File Size : 43,6 Mb
Release : 2016-06-20
Category : Computers
ISBN : 9783642319334

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Turing Computability by Robert I. Soare Pdf

Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author has honed the content over decades according to feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.

Author : Steven Homer,Alan L. Selman
Publisher : Springer Science & Business Media
Page : 206 pages
File Size : 51,6 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9781475735444

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Computability and Complexity Theory by Steven Homer,Alan L. Selman Pdf

Intended for use in an introductory graduate course in theoretical computer science, this text contains material that should be core knowledge in the theory of computation for all graduates in computer science. It is self-contained and is best suited for a one semester course. The text starts with classical computability theory which forms the basis for complexity theory. This has the pedagogical advantage that students learn a qualitative subject before advancing to a quantitative one. Since this is a graduate course, students should have some knowledge of such topics as automata theory, formal languages, computability theory, or complexity theory.

Author : Mikhail J. Atallah,Marina Blanton
Publisher : CRC Press
Page : 932 pages
File Size : 48,5 Mb
Release : 2009-11-20
Category : Computers
ISBN : 9781584888215

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Algorithms and Theory of Computation Handbook, Volume 2 by Mikhail J. Atallah,Marina Blanton Pdf

Algorithms and Theory of Computation Handbook, Second Edition: Special Topics and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems.Along with updating and revising many of

Author : S.B. Cooper,Benedikt Löwe,Andrea Sorbi
Publisher : Springer Science & Business Media
Page : 560 pages
File Size : 48,9 Mb
Release : 2007-11-28
Category : Computers
ISBN : 9780387685465

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New Computational Paradigms by S.B. Cooper,Benedikt Löwe,Andrea Sorbi Pdf

This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.

Author : E.R. Griffor
Publisher : Elsevier
Page : 724 pages
File Size : 40,9 Mb
Release : 1999-10-01
Category : Mathematics
ISBN : 0080533043

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Handbook of Computability Theory by E.R. Griffor Pdf

The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.

Author : Mikhail J. Atallah,Marina Blanton
Publisher : CRC Press
Page : 974 pages
File Size : 54,9 Mb
Release : 2009-11-20
Category : Computers
ISBN : 9781584888239

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Algorithms and Theory of Computation Handbook, Volume 1 by Mikhail J. Atallah,Marina Blanton Pdf

Algorithms and Theory of Computation Handbook, Second Edition: General Concepts and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many

Author : Marcella Anselmo,Gianluca Della Vedova,Florin Manea,Arno Pauly
Publisher : Springer Nature
Page : 379 pages
File Size : 46,8 Mb
Release : 2020-06-23
Category : Computers
ISBN : 9783030514662

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Beyond the Horizon of Computability by Marcella Anselmo,Gianluca Della Vedova,Florin Manea,Arno Pauly Pdf

This book constitutes the proceedings of the 16th Conference on Computability in Europe, CiE 2020, which was planned to be held in Fisciano, Italy, during June 29 until July 3, 2020. The conference moved to a virtual format due to the coronavirus pandemic. The 30 full and 5 short papers presented in this volume were carefully reviewed and selected from 72 submissions. CiE promotes the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2020 had as its motto Beyond the Horizon of Computability, reflecting the interest of CiE in research transgressing the traditional boundaries of computability theory.

Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 44,5 Mb
Release : 2019-10-29
Category : Computers
ISBN : 9780691189130

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Mathematics and Computation by Avi Wigderson Pdf

An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Author : Jens Blanck,Vasco Brattka
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 46,5 Mb
Release : 2001-05-23
Category : Computers
ISBN : 9783540421979

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Computability and Complexity in Analysis by Jens Blanck,Vasco Brattka Pdf

This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Computability and Complexity in Analysis, CCA 2000, held in Swansea, UK, in September 2000. The 23 revised full papers presented together with a report on a competition of exact real arithmetic systems were carefully selected from 28 papers accepted for presentation during the workshop. The book presents a cross-section on current research on computability and complexity in analysis.

Author : Gianluca Della Vedova,Besik Dundua,Steffen Lempp,Florin Manea
Publisher : Springer Nature
Page : 327 pages
File Size : 40,9 Mb
Release : 2023-07-18
Category : Computers
ISBN : 9783031369780

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Unity of Logic and Computation by Gianluca Della Vedova,Besik Dundua,Steffen Lempp,Florin Manea Pdf

This book constitutes the refereed proceedings of the 19th International Conference on Unity of Logic and Computation, CiE 2023, held in Batumi, Georgia, during July 24–28, 2023. The 23 full papers and 13 invited papers included in this book were carefully reviewed and selected from 51 submissions. They were organized in topical sections as follows: ​Degree theory; Proof Theory; Computability; Algorithmic Randomness; Computational Complexity; Interactive proofs; and Combinatorial approaches.