Computability In Context

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Computability in Context

Author : S Barry Cooper
Publisher : World Scientific
ISBN 13 : 1908978767
Total Pages : 420 pages
Book Rating : 4.9/5 (89 download)

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Book Synopsis Computability in Context by : S Barry Cooper

Download or read book Computability in Context written by S Barry Cooper and published by World Scientific. This book was released on 2011-02-25 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier. This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues, covering problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world, and how this affects our way of thinking about everyday computational issues. Contents:Computation, Information, and the Arrow of Time (P Adriaans & P van Emde Boas)The Isomorphism Conjecture for NP (M Agrawal)The Ershov Hierarchy (M M Arslanov)Complexity and Approximation in Reoptimization (G Ausiello et al.)Definability in the Real Universe (S B Cooper)HF-Computability (Y L Drshov et al.)The Mathematics of Computing Between Logic and Physics (G Longo & T Paul)Liquid State Machines: Motivation, Theory, and Applications (W Maass)Experiments on an Internal Approach to Typed Algorithms in Analysis (D Normann)Recursive Functions: An Archeological Look (P Odifreddi)Reverse Mathematics and Well-Ordering Principles (M Rathjen & A Weiermann)Discrete Transfinite Computation Models (P D Welch) Readership: Researchers in computational mathematics, logic, and theoretical computer science. Keywords:Computability;Logic;Real World;Turing Barrier;Real Computation;Learning Theory

Computability, Complexity, and Languages

Author : Martin Davis
Publisher : Academic Press
ISBN 13 : 0122063821
Total Pages : 631 pages
Book Rating : 4.1/5 (22 download)

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Book Synopsis Computability, Complexity, and Languages by : Martin Davis

Download or read book Computability, Complexity, and Languages written by Martin Davis and published by Academic Press. This book was released on 1994-02-03 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text covers the key areas of computer science, including recursive function theory, formal languages, and automata. Additions to the second edition include: extended exercise sets, which vary in difficulty; expanded section on recursion theory; new chapters on program verification and logic programming; updated references and examples throughout.

The Foundations of Computability Theory

Author : Borut Robič
Publisher : Springer
ISBN 13 : 3662448084
Total Pages : 331 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis The Foundations of Computability Theory by : Borut Robič

Download or read book The Foundations of Computability Theory written by Borut Robič and published by Springer. This book was released on 2015-09-14 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.

Automata and Computability

Author : Dexter C. Kozen
Publisher : Springer
ISBN 13 : 364285706X
Total Pages : 399 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Automata and Computability by : Dexter C. Kozen

Download or read book Automata and Computability written by Dexter C. Kozen and published by Springer. This book was released on 2013-11-11 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are my lecture notes from CS381/481: Automata and Computability Theory, a one-semester senior-level course I have taught at Cornell Uni versity for many years. I took this course myself in thc fall of 1974 as a first-year Ph.D. student at Cornell from Juris Hartmanis and have been in love with the subject ever sin,:e. The course is required for computer science majors at Cornell. It exists in two forms: CS481, an honors version; and CS381, a somewhat gentler paced version. The syllabus is roughly the same, but CS481 go es deeper into thc subject, covers more material, and is taught at a more abstract level. Students are encouraged to start off in one or the other, then switch within the first few weeks if they find the other version more suitaLle to their level of mathematical skill. The purpose of t.hc course is twofold: to introduce computer science students to the rieh heritage of models and abstractions that have arisen over the years; and to dew!c'p the capacity to form abstractions of their own and reason in terms of them.

Models of Computation in Context

Author : Benedikt Löwe
Publisher : Springer
ISBN 13 : 364221875X
Total Pages : 319 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Models of Computation in Context by : Benedikt Löwe

Download or read book Models of Computation in Context written by Benedikt Löwe and published by Springer. This book was released on 2011-09-15 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th Conference on Computability in Europe, CiE 2011, held in Sofia, Bulgaria, in June/July 2011. The 22 revised papers presented together with 11 invited lectures were carefully reviewed and selected with an acceptance rate of under 40%. The papers cover the topics computability in analysis, algebra, and geometry; classical computability theory; natural computing; relations between the physical world and formal models of computability; theory of transfinite computations; and computational linguistics.

Higher-Order Computability

Author : John Longley
Publisher : Springer
ISBN 13 : 3662479923
Total Pages : 571 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Higher-Order Computability by : John Longley

Download or read book Higher-Order Computability written by John Longley and published by Springer. This book was released on 2015-11-06 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Computability Theory

Author : S. Barry Cooper
Publisher : CRC Press
ISBN 13 : 1420057561
Total Pages : 420 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Computability Theory by : S. Barry Cooper

Download or read book Computability Theory written by S. Barry Cooper and published by CRC Press. This book was released on 2017-09-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.

Computability Theory

Author : Herbert B. Enderton
Publisher : Academic Press
ISBN 13 : 9780123849595
Total Pages : 192 pages
Book Rating : 4.8/5 (495 download)

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Book Synopsis Computability Theory by : Herbert B. Enderton

Download or read book Computability Theory written by Herbert B. Enderton and published by Academic Press. This book was released on 2010-12-30 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability Theory: An Introduction to Recursion Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way. Frequent historical information presented throughout More extensive motivation for each of the topics than other texts currently available Connects with topics not included in other textbooks, such as complexity theory

Models of Computation

Author : Maribel Fernandez
Publisher : Springer Science & Business Media
ISBN 13 : 1848824343
Total Pages : 184 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Models of Computation by : Maribel Fernandez

Download or read book Models of Computation written by Maribel Fernandez and published by Springer Science & Business Media. This book was released on 2009-04-14 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An in-depth analysis of the basic concepts underlying each model of computation is provided. Divided into two parts, the first highlights the traditional computation models used in the first studies on computability: - Automata and Turing Machines; - Recursive functions and the Lambda-Calculus; - Logic-based computation models. and the second part covers object-oriented and interaction-based models. There is also a chapter on concurrency, and a final chapter on emergent computation models inspired by quantum mechanics. At the end of each chapter there is a discussion on the use of computation models in the design of programming languages.

A Programming Approach to Computability

Author : A.J. Kfoury
Publisher : Springer Science & Business Media
ISBN 13 : 1461257492
Total Pages : 259 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis A Programming Approach to Computability by : A.J. Kfoury

Download or read book A Programming Approach to Computability written by A.J. Kfoury and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability theory is at the heart of theoretical computer science. Yet, ironically, many of its basic results were discovered by mathematical logicians prior to the development of the first stored-program computer. As a result, many texts on computability theory strike today's computer science students as far removed from their concerns. To remedy this, we base our approach to computability on the language of while-programs, a lean subset of PASCAL, and postpone consideration of such classic models as Turing machines, string-rewriting systems, and p. -recursive functions till the final chapter. Moreover, we balance the presentation of un solvability results such as the unsolvability of the Halting Problem with a presentation of the positive results of modern programming methodology, including the use of proof rules, and the denotational semantics of programs. Computer science seeks to provide a scientific basis for the study of information processing, the solution of problems by algorithms, and the design and programming of computers. The last 40 years have seen increasing sophistication in the science, in the microelectronics which has made machines of staggering complexity economically feasible, in the advances in programming methodology which allow immense programs to be designed with increasing speed and reduced error, and in the develop ment of mathematical techniques to allow the rigorous specification of program, process, and machine.

Automata, Computability and Complexity

Author : Elaine Rich
Publisher : Prentice Hall
ISBN 13 : 0132288060
Total Pages : 1120 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Automata, Computability and Complexity by : Elaine Rich

Download or read book Automata, Computability and Complexity written by Elaine Rich and published by Prentice Hall. This book was released on 2008 with total page 1120 pages. Available in PDF, EPUB and Kindle. Book excerpt: For upper level courses on Automata. Combining classic theory with unique applications, this crisp narrative is supported by abundant examples and clarifies key concepts by introducing important uses of techniques in real systems. Broad-ranging coverage allows instructors to easily customise course material to fit their unique requirements.

Computability Theory

Author : S. Barry Cooper
Publisher : CRC Press
ISBN 13 : 1351991965
Total Pages : 420 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis Computability Theory by : S. Barry Cooper

Theories of Computability

Author : Nicholas Pippenger
Publisher : Cambridge University Press
ISBN 13 : 9780521553803
Total Pages : 268 pages
Book Rating : 4.5/5 (538 download)

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Book Synopsis Theories of Computability by : Nicholas Pippenger

Download or read book Theories of Computability written by Nicholas Pippenger and published by Cambridge University Press. This book was released on 1997-05-28 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically sophisticated introduction to Turing's theory, Boolean functions, automata, and formal languages.

The Foundations of Computability Theory

Author : Borut Robič
Publisher : Springer Nature
ISBN 13 : 3662624214
Total Pages : 422 pages
Book Rating : 4.6/5 (626 download)

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Book Synopsis The Foundations of Computability Theory by : Borut Robič

Download or read book The Foundations of Computability Theory written by Borut Robič and published by Springer Nature. This book was released on 2020-11-13 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism. In Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability. In Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.

Computability and Complexity

Author : Neil D. Jones
Publisher : MIT Press
ISBN 13 : 9780262100649
Total Pages : 494 pages
Book Rating : 4.1/5 (6 download)

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Book Synopsis Computability and Complexity by : Neil D. Jones

Download or read book Computability and Complexity written by Neil D. Jones and published by MIT Press. This book was released on 1997 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine- and G�del number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems. According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models. New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs. Foundations of Computing series

Automata and Computability

Author : Ganesh Gopalakrishnan
Publisher : CRC Press
ISBN 13 : 1351374281
Total Pages : 375 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Automata and Computability by : Ganesh Gopalakrishnan

Download or read book Automata and Computability written by Ganesh Gopalakrishnan and published by CRC Press. This book was released on 2019-03-04 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automata and Computability is a class-tested textbook which provides a comprehensive and accessible introduction to the theory of automata and computation. The author uses illustrations, engaging examples, and historical remarks to make the material interesting and relevant for students. It incorporates modern/handy ideas, such as derivative-based parsing and a Lambda reducer showing the universality of Lambda calculus. The book also shows how to sculpt automata by making the regular language conversion pipeline available through a simple command interface. A Jupyter notebook will accompany the book to feature code, YouTube videos, and other supplements to assist instructors and students Features Uses illustrations, engaging examples, and historical remarks to make the material accessible Incorporates modern/handy ideas, such as derivative-based parsing and a Lambda reducer showing the universality of Lambda calculus Shows how to "sculpt" automata by making the regular language conversion pipeline available through simple command interface Uses a mini functional programming (FP) notation consisting of lambdas, maps, filters, and set comprehension (supported in Python) to convey math through PL constructs that are succinct and resemble math Provides all concepts are encoded in a compact Functional Programming code that will tesselate with Latex markup and Jupyter widgets in a document that will accompany the books. Students can run code effortlessly href="https://github.com/ganeshutah/Jove.git/"here.

Computability

Author : Richard L Epstein
Publisher : Advanced Reasoning Forum
ISBN 13 : 0981550738
Total Pages : 382 pages
Book Rating : 4.9/5 (815 download)

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Book Synopsis Computability by : Richard L Epstein

Download or read book Computability written by Richard L Epstein and published by Advanced Reasoning Forum. This book was released on 2018-10-24 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in a new edition!--the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".