Computability theory theory turing (46 Ergebnisse)

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Turing'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 IIincludes 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 has honed the content over decades according to 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.…

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Taschenbuch. Zustand: Neu. Turing Computability | Theory and Applications | Robert I. Soare | Taschenbuch | Theory and Applications of Computability | xxxvi | Englisch | 2018 | Springer | EAN 9783662568583 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.…

Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Turing'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 IIincludes 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 has honed the content over decades according to 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.…

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Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems. It can be visualized as a Turing machine with a black box, called an oracle, which is able to decide certain decision problems in a single operation. The problem can be of any complexity class. Even undecidable problems, like the halting problem, can be used.An oracle machine is a Turing machine connected to an oracle. The oracle, in this context, is thought of as an entity capable of answering some collection of questions, and usually represented as some subset A of the natural numbers. Intuitively then, the oracle machine can perform all of the usual operations of a Turing machine, and can also query the oracle for an answer to a specific question of the form 'is x in A ' There are several different definitions of an oracle machine, all of which are equivalent in the sense that they agree on when a specific function f can be computed by an oracle machine with oracle A.…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! The theory of computation is the branch of computer science and mathematics that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into two major branches: computability theory and complexity theory, but both branches deal with formal models of computation. In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most commonly examined is the Turing machine. A Turing machine can be thought of as a desktop PC with a potentially infinite memory capacity, though it can only access this memory in small discrete chunks.…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! A computational system that can compute every Turing-computable function is called Turing-complete (or Turing-powerful). Alternatively, such a system is one that can simulate a universal Turing machine.A Turing-complete system is called Turing-equivalent if every function it can compute is also Turing-computable; i.e., it computes precisely the same class of functions as do Turing machines. Alternatively, a Turing-equivalent system is one that can simulate, and be simulated by, a universal Turing machine. (All known Turing-complete systems are Turing-equivalent, which adds support to the Church-Turing thesis.).…

Taschenbuch. Zustand: Neu. Computability Theory | Computability theory. Turing reduction, Turing degree, Reduction (recursion theory), Reverse mathematics, Kolmogorov complexity, Recursion (computer science) | Frederic P. Miller (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130066277 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In computability theory, super-recursive algorithms are a generalization of ordinary algorithms that are more powerful, that is, compute more than Turing machines. The term was introduced by Mark Burgin, whose book 'Super-recursive algorithms' develops their theory and presents several mathematical models. Turing machines and other mathematical models of conventional algorithms allow researchers to find properties of recursive algorithms and their computations. In a similar way, mathematical models of super-recursive algorithms, such as inductive Turing machines, allow researchers to find properties of super-recursive algorithms and their computations.…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In computabilitytheory and computational complexity theory, a many-one reduction is areduction which converts instances of one decision problem intoinstances of a second decision problem. Reductions are thus used tomeasure the relative computational difficulty of two problems. Many-onereductions are a special case and a stronger form of Turing reductions.With many-one reductions the oracle can be invoked only once at the endand the answer cannot be modified. Many-one reductions were first usedby Emil Post in 1944. Later Norman Shapiro used the same concept in 1956under the name strong reducibility.…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In computabilitytheory and computational complexity theory, a reduction is atransformation of one problem into another problem. Depending on thetransformation used this can be used to define complexity classes on aset of problems. Intuitively, problem A is reducible to problem B ifsolutions to B exist and give solutions to A whenever A has solutions.Thus, solving A cannot be harder than solving B. We write A ¿m Busually with a subscript on the ¿ to indicate the type of reductionbeing used (m : mapping reduction,p : polynomial reduction).…

Taschenbuch. Zustand: Neu. Turing degree | Computer Science, Mathematical Logic, Computability Theory, Partially Ordered Set, Turing Reduction, Oracle Machine, Equivalence Relation, Equivalence Class, Many-One Reduction | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130353605 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.…