Computability Enumerability Unsolvability

Author : S. B. Cooper
Publisher : Cambridge University Press
ISBN 13 : 0521557364
Total Pages : 359 pages
Book Rating : 4.68/5 ( download)

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Download or read book Computability, Enumerability, Unsolvability written by S. B. Cooper and published by Cambridge University Press. This book was released on 1996-01-11 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will make this volume an invaluable resource.

Author : S. Barry Cooper
Publisher :
ISBN 13 : 9781107362390
Total Pages : 357 pages
Book Rating : 4.93/5 ( download)

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Download or read book Computability, Enumerability, Unsolvability written by S. Barry Cooper and published by . This book was released on 2014-05-14 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory.

Author : Martin Davis
Publisher : Courier Corporation
ISBN 13 : 0486614719
Total Pages : 292 pages
Book Rating : 4.17/5 ( download)

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Download or read book Computability & Unsolvability written by Martin Davis and published by Courier Corporation. This book was released on 1982-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.

Author : Hans Hermes
Publisher : Springer Science & Business Media
ISBN 13 : 3642461786
Total Pages : 260 pages
Book Rating : 4.81/5 ( download)

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Download or read book Enumerability · Decidability Computability written by Hans Hermes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Once we have accepted a precise replacement of the concept of algo rithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algo rithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathe matics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms.

Author : Hans Hermes
Publisher : Springer
ISBN 13 : 3662116863
Total Pages : 255 pages
Book Rating : 4.69/5 ( download)

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Download or read book Enumerability, Decidability, Computability written by Hans Hermes and published by Springer. This book was released on 2013-03-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The task of developing algorithms to solve problems has always been considered by mathematicians to be an especially interesting and im portant one. Normally an algorithm is applicable only to a narrowly limited group of problems. Such is for instance the Euclidean algorithm, which determines the greatest common divisor of two numbers, or the well-known procedure which is used to obtain the square root of a natural number in decimal notation. The more important these special algorithms are, all the more desirable it seems to have algorithms of a greater range of applicability at one's disposal. Throughout the centuries, attempts to provide algorithms applicable as widely as possible were rather unsuc cessful. It was only in the second half of the last century that the first appreciable advance took place. Namely, an important group of the inferences of the logic of predicates was given in the form of a calculus. (Here the Boolean algebra played an essential pioneer role. ) One could now perhaps have conjectured that all mathematical problems are solvable by algorithms. However, well-known, yet unsolved problems (problems like the word problem of group theory or Hilbert's tenth problem, which considers the question of solvability of Diophantine equations) were warnings to be careful. Nevertheless, the impulse had been given to search for the essence of algorithms. Leibniz already had inquired into this problem, but without success.

Author : Martin Davis
Publisher :
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.64/5 ( download)

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Download or read book Computability & Unsolvability written by Martin Davis and published by . This book was released on 1958 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Martin Davis
Publisher : Courier Corporation
ISBN 13 : 0486151069
Total Pages : 292 pages
Book Rating : 4.69/5 ( download)

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Download or read book Computability and Unsolvability written by Martin Davis and published by Courier Corporation. This book was released on 2013-04-16 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.

Author : Robert I. Soare
Publisher : Springer
ISBN 13 : 3642319335
Total Pages : 289 pages
Book Rating : 4.34/5 ( download)

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Download or read book Turing Computability written by Robert I. Soare and published by Springer. This book was released on 2016-06-20 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : T. N. Srivastava
Publisher : Tata McGraw-Hill Education
ISBN 13 : 9780070159105
Total Pages : 0 pages
Book Rating : 4.06/5 ( download)

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Download or read book Business Research Methodology (With Cd) written by T. N. Srivastava and published by Tata McGraw-Hill Education. This book was released on 1958 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.

Author : Kurt Gödel
Publisher : Courier Corporation
ISBN 13 : 0486158403
Total Pages : 82 pages
Book Rating : 4.02/5 ( download)

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Download or read book On Formally Undecidable Propositions of Principia Mathematica and Related Systems written by Kurt Gödel and published by Courier Corporation. This book was released on 2012-05-24 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.