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020 _a9783662448083
_z978-3-662-44808-3
024 7 _a10.1007/978-3-662-44808-3
_2doi
050 4 _aQA75.5-76.95
072 7 _aUY
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aUY
_2thema
072 7 _aUYA
_2thema004.0151
_223
100 1 _aRobič, Borut.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Foundations of Computability Theory /
_cby Borut Robič.
250 _a1st ed. 2015.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2015.
300 _a1 online resource
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
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 _aInformation theory.
650 0 _aComputer science.
650 0 _aComputer science
_xMathematics.
650 1 4 _aTheory of Computation.
_0http://scigraph.springernature.com/things/product-market-codes/I16005
650 2 4 _aMathematics of Computing.
_0http://scigraph.springernature.com/things/product-market-codes/I17001
650 2 4 _aComputational Mathematics and Numerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M1400X
710 2 _aSpringerLink (Online service)
856 4 0 _uhttps://doi.org/10.1007/978-3-662-44808-3
_3Springer eBooks
_zOnline access link to the resource
912 _aZDB-2-SCS
999 _c200433927
_d52139
942 _2lcc
_cEBK
041 _aeng