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001			394856
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008			220802s2022 sz | s |||| 0|eng d
020			_a9783030832025
024	7		_a10.1007/978-3-030-83202-5 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC
100	1		_aTourlakis, George _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	0	_aComputability _cby George Tourlakis
250			_a1st edition 2022
264		1	_aCham _bSpringer International Publishing _c2022
300			_a1 recurso en línea (XXVII, 637 páginas) _b12 ilustraciones, 10 ilustraciones a color
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
505	0		_aMathematical Background; a Review -- A Theory of Computability -- Primitive Recursive Functions -- Loop Programs.-The Ackermann Function -- (Un)Computability via Church's Thesis -- Semi-Recursiveness -- Yet another number-theoretic characterisation of P -- Godel's Incompleteness Theorem via the Halting Problem -- The Recursion Theorem -- A Universal (non-PR) Function for PR -- Enumerations of Recursive and Semi-Recursive Sets -- Creative and Productive Sets Completeness -- Relativised Computability -- POSSIBILITY: Complexity of P Functions -- Complexity of PR Functions -- Turing Machines and NP-Completeness.
520			_aThis survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of "mechanical process" using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. Features: Extensive and mathematically complete coverage of the limitations of logic, including Gödel's incompleteness theorems (first and second), Rosser's version of the first incompleteness theorem, and Tarski's non expressibility of "truth" Inability of computability to detect formal theorems effectively, using Church's proof of the unsolvability of Hilbert's Entscheidungsproblem Arithmetisation-free proof of the pillars of computability: Kleene's s-m-n, universal function and normal form theorems - using "Church's thesis" and a simulation of the URM ("register machine") by a simultaneous recursion. These three pivotal results lead to the deeper results of the theory Extensive coverage of the advanced topic of computation with "oracles" including an exposition of the search computability theory of Moschovakis, the first recursion theorem, Turing reducibility and Turing degrees and an application of the Sacks priority method of "preserving agreements", and the arithmetical hierarchy including Post's theorem Cobham's mathematical characterisation of the concept deterministic polynomial time computable function is fully proved A complete proof of Blum's speed-up theorem.
776	0	8	_iPrinted edition: _z9783030832018
776	0	8	_iPrinted edition: _z9783030832032
776	0	8	_iPrinted edition: _z9783030832049
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-030-83202-5 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
988			_aSpringer_Computer_2022
999			_c394856 _d394856