000 | 04326nam a22005655i 4500 | ||
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001 | 978-3-030-83202-5 | ||
003 | DE-He213 | ||
005 | 20240423125455.0 | ||
007 | cr nn 008mamaa | ||
008 | 220802s2022 sz | s |||| 0|eng d | ||
020 |
_a9783030832025 _9978-3-030-83202-5 |
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024 | 7 |
_a10.1007/978-3-030-83202-5 _2doi |
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050 | 4 | _aQA75.5-76.95 | |
072 | 7 |
_aUYA _2bicssc |
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_aCOM014000 _2bisacsh |
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_aUYA _2thema |
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082 | 0 | 4 |
_a004.0151 _223 |
100 | 1 |
_aTourlakis, George. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aComputability _h[electronic resource] / _cby George Tourlakis. |
250 | _a1st ed. 2022. | ||
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2022. |
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300 |
_aXXVII, 637 p. 12 illus., 10 illus. in color. _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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_atext file _bPDF _2rda |
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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. | ||
650 | 0 | _aComputer science. | |
650 | 0 | _aComputable functions. | |
650 | 0 | _aRecursion theory. | |
650 | 0 | _aComputational complexity. | |
650 | 0 |
_aTechnology _xPhilosophy. |
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650 | 1 | 4 | _aTheory of Computation. |
650 | 2 | 4 | _aComputability and Recursion Theory. |
650 | 2 | 4 | _aComputational Complexity. |
650 | 2 | 4 | _aModels of Computation. |
650 | 2 | 4 | _aPhilosophy of Technology. |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer Nature eBook | |
776 | 0 | 8 |
_iPrinted edition: _z9783030832018 |
776 | 0 | 8 |
_iPrinted edition: _z9783030832032 |
776 | 0 | 8 |
_iPrinted edition: _z9783030832049 |
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-030-83202-5 |
912 | _aZDB-2-SCS | ||
912 | _aZDB-2-SXCS | ||
942 | _cSPRINGER | ||
999 |
_c178318 _d178318 |