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| Author | : Hartley Rogers |
| Publisher | : National Geographic Books |
| Total Pages | : 0 |
| Release | : 1987-04-22 |
| Genre | : Computers |
| ISBN | : 0262680521 |
(Reprint of the 1967 edition)
| Author | : Hartley Rogers (Jr.) |
| Publisher | : |
| Total Pages | : 482 |
| Release | : 1967 |
| Genre | : |
| ISBN | : |
| Author | : Hartley Rogers |
| Publisher | : |
| Total Pages | : 526 |
| Release | : 1967 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Nigel Cutland |
| Publisher | : Cambridge University Press |
| Total Pages | : 268 |
| Release | : 1980-06-19 |
| Genre | : Computers |
| ISBN | : 9780521294652 |
What can computers do in principle? What are their inherent theoretical limitations? The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function - a function whose values can be calculated in an automatic way.
| Author | : Robert I. Soare |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 460 |
| Release | : 1999-11-01 |
| Genre | : Mathematics |
| ISBN | : 9783540152996 |
..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988
| Author | : Neil D. Jones |
| Publisher | : Academic Press |
| Total Pages | : 169 |
| Release | : 2014-06-20 |
| Genre | : Mathematics |
| ISBN | : 1483218481 |
Computability Theory: An Introduction provides information pertinent to the major concepts, constructions, and theorems of the elementary theory of computability of recursive functions. This book provides mathematical evidence for the validity of the Church–Turing thesis. Organized into six chapters, this book begins with an overview of the concept of effective process so that a clear understanding of the effective computability of partial and total functions is obtained. This text then introduces a formal development of the equivalence of Turing machine computability, enumerability, and decidability with other formulations. Other chapters consider the formulas of the predicate calculus, systems of recursion equations, and Post's production systems. This book discusses as well the fundamental properties of the partial recursive functions and the recursively enumerable sets. The final chapter deals with different formulations of the basic ideas of computability that are equivalent to Turing-computability. This book is a valuable resource for undergraduate or graduate students.
| Author | : Peter Smith |
| Publisher | : Cambridge University Press |
| Total Pages | : 376 |
| Release | : 2007-07-26 |
| Genre | : Mathematics |
| ISBN | : 0521857848 |
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
| Author | : Nigel Cutland |
| Publisher | : Cambridge University Press |
| Total Pages | : 268 |
| Release | : 1980-06-19 |
| Genre | : Computers |
| ISBN | : 1139935607 |
What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gödel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest.
| Author | : Piergiorgio Odifreddi |
| Publisher | : |
| Total Pages | : 668 |
| Release | : 1999 |
| Genre | : Recursion theory |
| ISBN | : 9780444589439 |
| Author | : Robert I. Soare |
| Publisher | : Springer |
| Total Pages | : 263 |
| Release | : 2016-06-20 |
| Genre | : Computers |
| ISBN | : 3642319335 |
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 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 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.
