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Turing computability [electronic resource] : theory and applications

Turing computability [electronic resource] : theory and applications

자료유형
E-Book(소장)
개인저자
Soare, R. I. (Robert Irving), 1940-.
서명 / 저자사항
Turing computability [electronic resource] : theory and applications / by Robert I. Soare.
발행사항
Berlin, Heidelberg :   Springer Berlin Heidelberg :   Imprint: Springer,   2016.  
형태사항
1 online resource (xxxvi, 263 p.) : ill.
총서사항
Theory and applications of computability, in cooperation with the association computability in Europe,2190-619X, ISSN 2190-6203 (electronic)
ISBN
9783642319334
요약
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 is a leading authority on the topic and he has taught the subject using the book content over decades, honing it according to experience and 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.
일반주기
Title from e-Book title page.  
내용주기
Part I Foundations of Computability -- Chap. 1 Defining Computability -- Chap. 2 Computably Enumerable Sets -- Chap. 3 Turing Reducibility -- Chap. 4 The Arithmetical Hierarchy -- Chap. 5 Classifying C.E. Sets -- Chap. 6 Oracle Constructions and Forcing -- Chap. 7 The Finite Injury Method -- Part II Trees and Π01 Classes -- Chap. 8 Open and Closed Classes -- Chap. 9 Basis Theorems -- Chap. 10 Peano Arithmetic and Π01-Classes -- Chap. 11 Randomness and Π01-Classes -- Part III Minimal Degrees -- Chap. 12 Minimal Degrees Below Øʹʹ -- Chap. 13 Minimal Degrees Below Øʹ -- Part IV Games in Computability Theory -- Chap. 14 Banach-Mazur Games -- Chap. 15 Gale-Stewart Games -- Chap. 16 More Lachlan Games -- Part V History of Computability -- Chap. 17 History of Computability -- References -- Index.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Computer science --Mathematics. Computable functions. Turing test. Logic, Symbolic and mathematical.
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006 m d
007 cr
008 200601s2016 sz a ob 001 0 eng d
020 ▼a 9783642319334
040 ▼a 211009 ▼c 211009 ▼d 211009
082 0 4 ▼a 004.0151 ▼2 23
084 ▼a 004.0151 ▼2 DDCK
090 ▼a 004.0151
100 1 ▼a Soare, R. I. ▼q (Robert Irving), ▼d 1940-.
245 1 0 ▼a Turing computability ▼h [electronic resource] : ▼b theory and applications / ▼c by Robert I. Soare.
260 ▼a Berlin, Heidelberg : ▼b Springer Berlin Heidelberg : ▼b Imprint: Springer, ▼c 2016.
300 ▼a 1 online resource (xxxvi, 263 p.) : ▼b ill.
490 1 ▼a Theory and applications of computability, in cooperation with the association computability in Europe, ▼x 2190-619X, ▼x ISSN 2190-6203 (electronic)
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a Part I Foundations of Computability -- Chap. 1 Defining Computability -- Chap. 2 Computably Enumerable Sets -- Chap. 3 Turing Reducibility -- Chap. 4 The Arithmetical Hierarchy -- Chap. 5 Classifying C.E. Sets -- Chap. 6 Oracle Constructions and Forcing -- Chap. 7 The Finite Injury Method -- Part II Trees and Π01 Classes -- Chap. 8 Open and Closed Classes -- Chap. 9 Basis Theorems -- Chap. 10 Peano Arithmetic and Π01-Classes -- Chap. 11 Randomness and Π01-Classes -- Part III Minimal Degrees -- Chap. 12 Minimal Degrees Below Øʹʹ -- Chap. 13 Minimal Degrees Below Øʹ -- Part IV Games in Computability Theory -- Chap. 14 Banach-Mazur Games -- Chap. 15 Gale-Stewart Games -- Chap. 16 More Lachlan Games -- Part V History of Computability -- Chap. 17 History of Computability -- References -- Index.
520 ▼a 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 is a leading authority on the topic and he has taught the subject using the book content over decades, honing it according to experience and 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Computer science ▼x Mathematics.
650 0 ▼a Computable functions.
650 0 ▼a Turing test.
650 0 ▼a Logic, Symbolic and mathematical.
830 0 ▼a Theory and applications of computability, in cooperation with the association computability in Europe.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-642-31933-4
945 ▼a KLPA
991 ▼a E-Book(소장)

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/e-Book 컬렉션/ 청구기호 CR 004.0151 등록번호 E14023382 도서상태 대출불가(열람가능) 반납예정일 예약 서비스 M

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