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Turing Computability = Theory and Ap...
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Turing Computability = Theory and Applications /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Turing Computability/ by Robert I. Soare.
其他題名:
Theory and Applications /
作者:
Soare, Robert I.
面頁冊數:
XXXVI, 263 p. 4 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Computers. -
電子資源:
https://doi.org/10.1007/978-3-642-31933-4
ISBN:
9783642319334
Turing Computability = Theory and Applications /
Soare, Robert I.
Turing Computability
Theory and Applications /[electronic resource] :by Robert I. Soare. - 1st ed. 2016. - XXXVI, 263 p. 4 illus.online resource. - Theory and Applications of Computability, In cooperation with the association Computability in Europe,2190-619X. - Theory and Applications of Computability, In cooperation with the association Computability in Europe,.
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.
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.
ISBN: 9783642319334
Standard No.: 10.1007/978-3-642-31933-4doiSubjects--Topical Terms:
565115
Computers.
LC Class. No.: QA75.5-76.95
Dewey Class. No.: 004.0151
Turing Computability = Theory and Applications /
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