{"product_id":"computability-hardcover","title":"Computability - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eGeorge Tourlakis\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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. \u003c\/p\u003e\u003cp\u003eAdvanced chapters cover the Ackerman function, Tarski's theorem on the non-representability of truth, Goedel's incompleteness and Rosser's incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church's thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum's complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003eFeatures: \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eExtensive 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 \u003ci\u003enon expressibility\u003c\/i\u003e of \"truth\"\u003c\/li\u003e\n\u003cli\u003eInability of computability to detect formal theorems effectively, using Church's proof of the unsolvability of Hilbert's \u003ci\u003eEntscheidungsproblem\u003c\/i\u003e\n\u003c\/li\u003e\n\u003cli\u003eArithmetisation-free proof of the pillars of computability: Kleene's \u003ci\u003es-m-n, universal function and normal form theorems\u003c\/i\u003e -- 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\u003c\/li\u003e\n\u003cli\u003eExtensive 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\u003c\/li\u003e\n\u003cli\u003eCobham's mathematical characterisation of the concept \u003ci\u003edeterministic polynomial time computable function\u003c\/i\u003e is fully proved\u003c\/li\u003e\n\u003cli\u003eA complete proof of Blum's speed-up theorem\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003eGeorge Tourlakis, PHD, is University Professor of Computer Science and Engineering at York University in Toronto, Canada. He has published extensively in his areas of research interest, which include calculational logic, modal logic, computability, and complexity theory. Dr. Tourlakis is the author of \u003ci\u003eTheory of Computation\u003c\/i\u003e and \u003ci\u003eMathematical Logic\u003c\/i\u003e, both published by Wiley, and \u003ci\u003eLectures in Logic and Set Theory; Volumes 1 and 2\u003c\/i\u003e (Cambridge University Press).\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 637\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.44 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e August 03, 2022\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47212948717817,"sku":"9783030832018","price":161.98,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/Zm9rRVZsYWdnRnlLUDdZRE1jb29KQT09.webp?v=1768099125","url":"https:\/\/bookscloud.io\/products\/computability-hardcover","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}