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Computability / by George Tourlakis

データ種別	電子ブック
版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	XXVII, 637 p. 12 illus., 10 illus. in color : online resource
著者標目	*Tourlakis, George author SpringerLink (Online service)

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URL	巻　次	配架場所	請求記号	登録番号	コメント	刷　年	状　態	利用注記	ISBN	予約	請求メモ
URL		射水-電子	007	EB0002569	Computer Scinece R0 2005-6,2022-3				9783030832025

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一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-83202-5
件　名	LCSH:Computer science LCSH:Computable functions LCSH:Recursion theory LCSH:Computational complexity LCSH:Technology -- Philosophy 全ての件名で検索 FREE:Theory of Computation FREE:Computability and Recursion Theory FREE:Computational Complexity FREE:Models of Computation FREE:Philosophy of Technology
分　類	LCC:QA75.5-76.95 DC23:004.0151
書誌ID	EB00001957
ISBN	9783030832025