Computability
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Computability Complexity And Languages
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Author : Martin Davis
language : en
Publisher: Academic Press
Release Date : 1994-02-03
Computability Complexity And Languages written by Martin Davis and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-03 with Computers categories.
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.
Computability
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Author : Douglas S. Bridges
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computability written by Douglas S. Bridges and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: A Mathematical Sketchbook provides a brief but rigorous introduction to the abstract theory of computation, sometimes also referred to as recursion theory. It develops major themes in computability theory, such as Rice's theorem and the recursion theorem, and provides a systematic account of Blum's complexity theory as well as an introduction to the theory of computable real numbers and functions. The book is intended as a university text, but it may also be used for self-study; appropriate exercises and solutions are included.
Computability
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Author : B. Jack Copeland
language : en
Publisher: MIT Press
Release Date : 2015-01-30
Computability written by B. Jack Copeland and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-30 with Computers categories.
Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics. Contributors Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani
Computability And Unsolvability
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Author : Martin Davis
language : en
Publisher: Courier Corporation
Release Date : 2013-04-16
Computability And Unsolvability written by Martin Davis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-16 with Mathematics categories.
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.
Computability And Logic
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Author : George S. Boolos
language : en
Publisher: Cambridge University Press
Release Date : 2007-09-17
Computability And Logic written by George S. Boolos and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-17 with Computers categories.
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.
Computability
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Author : Klaus Weihrauch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computability written by Klaus Weihrauch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Intends to lay a common basis for the different branches of recursion theory. Leads from the very basic theory to modern concepts of computability. Consists of three consecutive parts: 1. Basic Concepts of Computability. 2. Traditional Recursion Theory. 3. Unified Type 2 theory of constructivity and computability on Baire's space including a general the- ory of representations.
Computability And Models
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Author : Barry S. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computability And Models written by Barry S. Cooper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. The theme running through this collection of papers is that of the interaction between descriptions, in the form of formal theories, and the algorithmic content of what is described, namely of the modeLs of those theories. This appears most explicitly here in a number of valuable, and substantial, contributions to what has until recently been known as 'recursive model theory' - an area in which researchers from the former Soviet Union (in particular Novosibirsk) have been pre-eminent. There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world. And, of course, there are also articles concerned with the classical theory of computability, including the first widely available survey of work on quasi-reducibility. The contributors, all internationally recognised experts in their fields, have been associated with the three-year INTAS-RFBR Research Project "Com putability and Models" (Project No. 972-139), and most have participated in one or more of the various international workshops (in Novosibirsk, Heidelberg and Almaty) and otherresearch activities of the network.
Handbook Of Computability Theory
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Author : E.R. Griffor
language : en
Publisher: Elsevier
Release Date : 1999-10-01
Handbook Of Computability Theory written by E.R. Griffor and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-01 with Mathematics categories.
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.
Computability In Analysis And Physics
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Author : Marian B. Pour-El
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02
Computability In Analysis And Physics written by Marian B. Pour-El and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Mathematics categories.
The first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning.
Turing Computability
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Author : Robert I. Soare
language : en
Publisher: Springer
Release Date : 2016-06-20
Turing Computability written by Robert I. Soare and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Computers categories.
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.