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RT Book, Whole SR Electronic DC OPAC T1 Computability / by George Tourlakis A1 Tourlakis, George A1 SpringerLink (Online service) YR 2022 FD 2022 SP XXVII, 637 p. 12 illus., 10 illus. in color K1 Computer science K1 Computable functions K1 Recursion theory K1 Computational complexity K1 Technology -- Philosophy K1 Theory of Computation K1 Computability and Recursion Theory K1 Computational Complexity K1 Models of Computation K1 Philosophy of Technology ED 1st ed. 2022. PB Springer International Publishing : Imprint: Springer PP Cham SN 9783030832025 LA English (英語) CL LCC:QA75.5-76.95 CL DC23:004.0151 NO Mathematical 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 NO This 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 NO HTTP:URL=https://doi.org/10.1007/978-3-030-83202-5 NO 書誌ID=EB00001957; LK [E Book]https://doi.org/10.1007/978-3-030-83202-5 OL 30