000 04598nam a22005535i 4500
001 978-3-662-62421-0
003 DE-He213
005 20240423125253.0
007 cr nn 008mamaa
008 201113s2020 gw | s |||| 0|eng d
020 _a9783662624210
_9978-3-662-62421-0
024 7 _a10.1007/978-3-662-62421-0
_2doi
050 4 _aQA75.5-76.95
072 7 _aUYA
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aUYA
_2thema
082 0 4 _a004.0151
_223
100 1 _aRobič, Borut.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Foundations of Computability Theory
_h[electronic resource] /
_cby Borut Robič.
250 _a2nd ed. 2020.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2020.
300 _aXXI, 422 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPart 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 _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. 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 _aComputer science.
650 0 _aMathematical logic.
650 0 _aComputers
_xHistory.
650 0 _aMathematics.
650 0 _aHistory.
650 1 4 _aTheory of Computation.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aHistory of Computing.
650 2 4 _aHistory of Mathematical Sciences.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662624203
776 0 8 _iPrinted edition:
_z9783662624227
776 0 8 _iPrinted edition:
_z9783662624234
856 4 0 _uhttps://doi.org/10.1007/978-3-662-62421-0
912 _aZDB-2-SCS
912 _aZDB-2-SXCS
942 _cSPRINGER
999 _c176122
_d176122