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020 _a9783662448083
_9978-3-662-44808-3
024 7 _a10.1007/978-3-662-44808-3
_2doi
035 _ato000561564
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA75.5-76.95
072 7 _aUY
_2bicssc
072 7 _aUYA
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072 7 _aCOM014000
_2bisacsh
072 7 _aCOM031000
_2bisacsh
082 0 4 _a004.0151
_223
100 1 _aRobič, Borut.
_eauthor.
_9469354
245 1 4 _aThe Foundations of Computability Theory
_helectronic resource
_cby Borut Robič.
250 _a1st ed. 2015.
260 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2015.
300 _aXX, 331 p. 109 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
505 0 _aIntroduction -- The Foundational Crisis of Mathematics -- Formalism -- Hilbert’s Attempt at Recovery -- The Quest for a Formalization -- The Turing Machine -- The First Basic Results -- Incomputable Problems -- Methods of Proving the Incomputability -- 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 -- Further Reading -- App. A, Mathematical Background -- References -- Index.
520 _aThis 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. 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.
650 0 _aComputer Science.
_9155490
650 0 _acomputers.
_9460101
650 0 _aComputer science
_xMathematics.
_9304486
650 0 _aComputer mathematics.
_9460896
650 1 4 _aComputer Science.
_9155490
650 2 4 _aTheory of Computation.
_9303507
650 2 4 _aMathematics of Computing.
_9303612
650 2 4 _aComputational Mathematics and Numerical Analysis.
_9303505
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-662-44808-3
912 _aZDB-2-SCS
999 _c416401