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008 | 170213s2015 gw | s |||| 0|eng d | ||
020 |
_a9783662448083 _9978-3-662-44808-3 |
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024 | 7 |
_a10.1007/978-3-662-44808-3 _2doi |
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035 | _ato000561564 | ||
040 |
_aSpringer _cSpringer _dRU-ToGU |
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050 | 4 | _aQA75.5-76.95 | |
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_aUY _2bicssc |
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_aUYA _2bicssc |
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_aCOM031000 _2bisacsh |
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_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. |
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300 |
_aXX, 331 p. 109 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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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 |
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650 | 0 |
_acomputers. _9460101 |
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650 | 0 |
_aComputer science _xMathematics. _9304486 |
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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 |