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000756171 019__ $$a952973092
000756171 020__ $$a9783642319334$$q(electronic book)
000756171 020__ $$a3642319335$$q(electronic book)
000756171 020__ $$z9783642319327
000756171 0247_ $$a10.1007/978-3-642-31933-4$$2doi
000756171 035__ $$aSP(OCoLC)ocn952604274
000756171 035__ $$aSP(OCoLC)952604274$$z(OCoLC)952973092
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000756171 08204 $$a511.3/52$$223
000756171 1001_ $$aSoare, R. I.$$q(Robert Irving),$$d1940-$$eauthor.
000756171 24510 $$aTuring computability$$h[electronic resource] :$$btheory and applications /$$cRobert I. Soare.
000756171 264_1 $$aBerlin :$$bSpringer,$$c2016.
000756171 300__ $$a1 online resource (xxxvi, 263 pages) :$$billustrations.
000756171 336__ $$atext$$btxt$$2rdacontent
000756171 337__ $$acomputer$$bc$$2rdamedia
000756171 338__ $$aonline resource$$bcr$$2rdacarrier
000756171 4901_ $$aTheory and applications of computability,$$x2190-619X
000756171 504__ $$aIncludes bibliographical references.
000756171 506__ $$aAccess limited to authorized users.
000756171 520__ $$aTuring's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author is a leading authority on the topic and he has taught the subject using the book content over decades, honing it according to experience and feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.
000756171 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed June 30, 2016).
000756171 650_0 $$aComputable functions.
000756171 650_0 $$aComputer science$$xMathematics.
000756171 650_0 $$aTuring test.
000756171 77608 $$iPrint version:$$z9783642319327
000756171 830_0 $$aTheory and applications of computability.
000756171 852__ $$bebk
000756171 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-642-31933-4$$zOnline Access$$91397441.1
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000756171 980__ $$aBIB
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