東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

The foundations of computability theory

Robic, Borut.

Linked to FindBook

Google Book

Amazon

博客來

The foundations of computability theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	The foundations of computability theory/ by Borut Robic.
Author:	Robic, Borut.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2020.,
Description:	xxi, 422 p. :ill., digital ;24 cm.
[NT 15003449]:	Part I, The Roots of Computability Theory -- Introduction -- The Foundational Crisis of Mathematics -- Formalism -- Hilbert's Attempt at Recovery -- Part II, Classicial Computability Theory -- The Quest for a Formalization -- The Turing Machine -- The First Basic Results -- Incomputable Problems -- Methods of Proving Incomputability -- Part III, Relative Computability -- Computation with External Help -- Degrees of Unsolvability -- The Turing Hierarchy of Unsolvability -- The Class D of Degrees of Unsolvability -- C.E. Degrees and the Priority Method -- The Arithmetical Hierarchy -- Part IV, Back to the Roots -- Computability (Church-Turing) Thesis Revisited -- Further Reading -- App. A, Mathematical Background -- App. B, Notation Index -- Glossary -- References -- Index.
Contained By:	Springer Nature eBook
Subject:	Computable functions. -
Online resource:	https://doi.org/10.1007/978-3-662-62421-0
ISBN:	9783662624210

The foundations of computability theory
Robic, Borut.

The foundations of computability theory[electronic resource] /by Borut Robic. - Second edition. - Berlin, Heidelberg :Springer Berlin Heidelberg :2020. - xxi, 422 p. :ill., digital ;24 cm.

Part I, The Roots of Computability Theory -- Introduction -- The Foundational Crisis of Mathematics -- Formalism -- Hilbert's Attempt at Recovery -- Part II, Classicial Computability Theory -- The Quest for a Formalization -- The Turing Machine -- The First Basic Results -- Incomputable Problems -- Methods of Proving Incomputability -- Part III, Relative Computability -- Computation with External Help -- Degrees of Unsolvability -- The Turing Hierarchy of Unsolvability -- The Class D of Degrees of Unsolvability -- C.E. Degrees and the Priority Method -- The Arithmetical Hierarchy -- Part IV, Back to the Roots -- Computability (Church-Turing) Thesis Revisited -- Further Reading -- App. A, Mathematical Background -- App. B, Notation Index -- Glossary -- References -- Index.

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism. In Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability. In Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.

ISBN: 9783662624210

Standard No.: 10.1007/978-3-662-62421-0doiSubjects--Topical Terms:

559829
Computable functions.

LC Class. No.: QA76.63 / .R63 2020

Dewey Class. No.: 004.0151

The foundations of computability theory
LDR:03792nmm a2200349 a 4500 001 2256862
003 DE-He213
005 20201113080853.0
006 m d
007 cr nn 008maaau
008 220420s2020 gw s 0 eng d
020 $a 9783662624210 $q (electronic bk.)
020 $a 9783662624203 $q (paper)
024 7 $a 10.1007/978-3-662-62421-0 $2 doi
035 $a 978-3-662-62421-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA76.63 $b .R63 2020
072 7 $a UY $2 bicssc
072 7 $a COM014000 $2 bisacsh
072 7 $a UY $2 thema
072 7 $a UYA $2 thema
082 0 4 $a 004.0151 $2 23
090 $a QA76.63 $b .R654 2020
100 1 $a Robic, Borut. $3 2162478
245 1 4 $a The foundations of computability theory $h [electronic resource] / $c by Borut Robic.
250 $a Second edition.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2020.
300 $a xxi, 422 p. : $b ill., digital ; $c 24 cm.
505 0 $a Part I, The Roots of Computability Theory -- Introduction -- The Foundational Crisis of Mathematics -- Formalism -- Hilbert's Attempt at Recovery -- Part II, Classicial Computability Theory -- The Quest for a Formalization -- The Turing Machine -- The First Basic Results -- Incomputable Problems -- Methods of Proving Incomputability -- Part III, Relative Computability -- Computation with External Help -- Degrees of Unsolvability -- The Turing Hierarchy of Unsolvability -- The Class D of Degrees of Unsolvability -- C.E. Degrees and the Priority Method -- The Arithmetical Hierarchy -- Part IV, Back to the Roots -- Computability (Church-Turing) Thesis Revisited -- Further Reading -- App. A, Mathematical Background -- App. B, Notation Index -- Glossary -- References -- Index.
520 $a This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism. In Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability. In Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.
650 0 $a Computable functions. $3 559829
650 0 $a Computers. $3 544777
650 0 $a History. $3 516518
650 0 $a Logic, Symbolic and mathematical. $3 532051
650 0 $a Mathematics. $3 515831
650 1 4 $a Theory of Computation. $3 892514
650 2 4 $a Mathematical Logic and Foundations. $3 892656
650 2 4 $a History of Computing. $3 895944
650 2 4 $a History of Mathematical Sciences. $3 1530523
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-662-62421-0
950 $a Computer Science (SpringerNature-11645)