Higher Order Computability

Author : John Longley,Dag Normann
Publisher : Springer
Page : 571 pages
File Size : 50,6 Mb
Release : 2015-11-06
Category : Computers
ISBN : 9783662479926

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Higher-Order Computability by John Longley,Dag Normann Pdf

This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages. In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them. The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers

Author : E.R. Griffor
Publisher : Elsevier
Page : 741 pages
File Size : 51,9 Mb
Release : 1999-10-01
Category : Mathematics
ISBN : 9780080533049

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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 : Nigel Cutland
Publisher : Cambridge University Press
Page : 268 pages
File Size : 47,9 Mb
Release : 1980-06-19
Category : Computers
ISBN : 0521294657

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Computability by Nigel Cutland Pdf

What can computers do in principle? What are their inherent theoretical limitations? The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function - a function whose values can be calculated in an automatic way.

Author : Gianluca Della Vedova,Besik Dundua,Steffen Lempp,Florin Manea
Publisher : Springer Nature
Page : 327 pages
File Size : 50,9 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.

Author : André Nies
Publisher : OUP Oxford
Page : 450 pages
File Size : 46,5 Mb
Release : 2012-03-29
Category : Mathematics
ISBN : 9780191627880

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Computability and Randomness by André Nies Pdf

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.

Author : George S. Boolos,John P. Burgess,Richard C. Jeffrey
Publisher : Cambridge University Press
Page : 365 pages
File Size : 43,6 Mb
Release : 2007-09-17
Category : Computers
ISBN : 9780521877527

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Computability and Logic by George S. Boolos,John P. Burgess,Richard C. Jeffrey Pdf

This fifth edition of 'Computability and Logic' covers not just the staple topics of an intermediate logic course such as Godel's incompleteness theorems, but also optional topics that include Turing's theory of computability and Ramsey's theorem.

Author : George Boolos,Richard C. Jeffrey
Publisher : CUP Archive
Page : 284 pages
File Size : 41,8 Mb
Release : 1974-07-18
Category : Mathematics
ISBN : 052120402X

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Computability and Logic by George Boolos,Richard C. Jeffrey Pdf

Author : Jens Blanck,Vasco Brattka,Peter Hertling
Publisher : Springer
Page : 396 pages
File Size : 44,8 Mb
Release : 2003-06-29
Category : Computers
ISBN : 9783540453352

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

The workshop on Computability and Complexity in Analysis, CCA 2000, was hosted by the Department of Computer Science of the University of Wales Swansea, September 17{19, 2000. It was the fourth workshop in a successful series of workshops: CCA’95 in Hagen, Germany, CCA’96 in Trier, Germany, and CCA’98 in Brno, Czech Republic. About 40 participants from the countries United Kingdom, Germany, Japan, Italy, Russia, France, Denmark, Greece, and Ireland contributed to the success of this meeting. Altogether, 28 talkswere p- sented in Swansea. These proceedings include 23 papers which represent a cro- section through recent research on computability and complexity in analysis. The workshop succeeded in bringing together people interested in computability and complexity aspects of analysis and in exploring connections with nume- cal methods, physics and, of course, computer science. It was rounded o by a number of talks and papers on exact computer arithmetic and by a competition of v e implemented systems. A report on this competition has been included in these proceedings. We would like to thank the authors for their contributions and the referees for their careful work, and we hope for further inspiring and constructive meetings of the same kind. April 2001 Jens Blanck Vasco Brattka Peter Hertling Organization CCA2000was hosted by the Department of Computer Science of the University of Wales Swansea and took place on September 17{19, 2000.

Author : Steven Homer,Alan L. Selman
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 54,5 Mb
Release : 2011-12-09
Category : Computers
ISBN : 9781461406815

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

This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable. Substantial new content in this edition includes: a chapter on nonuniformity studying Boolean circuits, advice classes and the important result of Karp─Lipton. a chapter studying properties of the fundamental probabilistic complexity classes a study of the alternating Turing machine and uniform circuit classes. an introduction of counting classes, proving the famous results of Valiant and Vazirani and of Toda a thorough treatment of the proof that IP is identical to PSPACE With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool. Topics and features: Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner Provides key mathematical background information, including sections on logic and number theory and algebra Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes

Author : T.V. Gopal,Junzo Watada
Publisher : Springer
Page : 721 pages
File Size : 46,5 Mb
Release : 2019-04-10
Category : Computers
ISBN : 9783030148126

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Theory and Applications of Models of Computation by T.V. Gopal,Junzo Watada Pdf

This book constitutes the refereed proceedings of the 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019, held in Kitakyushu, Japan, in April 2019. The 43 revised full papers were carefully reviewed and selected from 60 submissions. The main themes of the selected papers are computability, computer science logic, complexity, algorithms, models of computation, and systems theory.

Author : Hubert Comon-Lundh,Claude Kirchner,Hélène Kirchner
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 48,6 Mb
Release : 2007-06-22
Category : Computers
ISBN : 9783540731467

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Rewriting, Computation and Proof by Hubert Comon-Lundh,Claude Kirchner,Hélène Kirchner Pdf

Jean-Pierre Jouannaud has played a leading role in the field of rewriting and its technology. This Festschrift volume, published to honor him on his 60th Birthday, includes 13 refereed papers by leading researchers, current and former colleagues. The papers are grouped in thematic sections on Rewriting Foundations, Proof and Computation, and a final section entitled Towards Safety and Security.

Author : Gordana Dodig-Crnkovic,Raffaela Giovagnoli
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 43,5 Mb
Release : 2013-03-21
Category : Technology & Engineering
ISBN : 9783642372254

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Computing Nature by Gordana Dodig-Crnkovic,Raffaela Giovagnoli Pdf

This book is about nature considered as the totality of physical existence, the universe, and our present day attempts to understand it. If we see the universe as a network of networks of computational processes at many different levels of organization, what can we learn about physics, biology, cognition, social systems, and ecology expressed through interacting networks of elementary particles, atoms, molecules, cells, (and especially neurons when it comes to understanding of cognition and intelligence), organs, organisms and their ecologies? Regarding our computational models of natural phenomena Feynman famously wondered: “Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?” Phenomena themselves occur so quickly and automatically in nature. Can we learn how to harness nature’s computational power as we harness its energy and materials? This volume includes a selection of contributions from the Symposium on Natural Computing/Unconventional Computing and Its Philosophical Significance, organized during the AISB/IACAP World Congress 2012, held in Birmingham, UK, on July 2-6, on the occasion of the centenary of Alan Turing’s birth. In this book, leading researchers investigated questions of computing nature by exploring various facets of computation as we find it in nature: relationships between different levels of computation, cognition with learning and intelligence, mathematical background, relationships to classical Turing computation and Turing’s ideas about computing nature - unorganized machines and morphogenesis. It addresses questions of information, representation and computation, interaction as communication, concurrency and agent models; in short this book presents natural computing and unconventional computing as extension of the idea of computation as symbol manipulation.

Author : Rosalie Iemhoff,Michael Moortgat,Ruy de Queiroz
Publisher : Springer
Page : 683 pages
File Size : 50,8 Mb
Release : 2019-06-23
Category : Mathematics
ISBN : 9783662595336

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Logic, Language, Information, and Computation by Rosalie Iemhoff,Michael Moortgat,Ruy de Queiroz Pdf

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 26th Workshop on Logic, Language, Information and Communication, WoLLIC 2019, held in Utrecht, The Netherlands, in July 2019. The 41 full papers together with 6 invited lectures presented were fully reviewed and selected from 60 submissions. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation, and yet is small enough to allow for concrete and useful interaction among participants.

Author : George Boolos
Publisher : Harvard University Press
Page : 458 pages
File Size : 40,9 Mb
Release : 1998
Category : Mathematics
ISBN : 067453767X

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Logic, Logic, and Logic by George Boolos Pdf

George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.

Author : Florin Manea,Barnaby Martin,Daniël Paulusma,Giuseppe Primiero
Publisher : Springer
Page : 336 pages
File Size : 53,9 Mb
Release : 2019-07-04
Category : Computers
ISBN : 9783030229962

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Computing with Foresight and Industry by Florin Manea,Barnaby Martin,Daniël Paulusma,Giuseppe Primiero Pdf

This book constitutes the refereed proceedings of the 15th Conference on Computability in Europe, CiE 2019, held in Durham, UK, in July 2019. The 20 revised full papers presented were carefully reviewed and selected from 35 submissions. In addition, this volume includes 7 invited papers. The conference CiE 2018 had the following six special sessions: computational neuroscience, history and philosophy of computing, lowness notions in computability, probabilistic programming and higher-order computation, smoothed and probabilistic analysis of algorithms, and transnite computations.