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Turing computability[electronic resource] :theory and applications /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	511.352
書名/作者:	Turing computability : theory and applications // by Robert I. Soare.
作者:	Soare, Robert I.
出版者:	Berlin, Heidelberg : : Springer Berlin Heidelberg :, 2016.
面頁冊數:	xxxvi, 263 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Computable functions.
標題:	Computer science - Mathematics.
標題:	Turing test.
標題:	Computer Science.
標題:	Theory of Computation.
標題:	Mathematics of Computing.
標題:	Mathematical Logic and Foundations.
ISBN:	9783642319334
ISBN:	9783642319327
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-642-31933-4

Turing computability[electronic resource] :theory and applications /
Soare, Robert I.

Turing computabilitytheory and applications /[electronic resource] :by Robert I. Soare. - Berlin, Heidelberg :Springer Berlin Heidelberg :2016. - xxxvi, 263 p. :ill., digital ;24 cm. - Theory and applications of computability,2190-619X. - Theory and applications of computability..

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:

461310
Computable functions.

LC Class. No.: QA9.59

Dewey Class. No.: 511.352

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