Computability Theory And Its Applications PDF Download
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| Author | : Peter Cholak |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 338 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821819224 |
Download Computability Theory and Its Applications Book in PDF, ePub and Kindle
This collection of articles presents a snapshot of the status of computability theory at the end of the millennium and a list of fruitful directions for future research. The papers represent the works of experts in the field who were invited speakers at the AMS-IMS-SIAM 1999 Summer Conference on Computability Theory and Applications, which focused on open problems in computability theory and on some related areas in which the ideas, methods, and/or results of computability theory play a role. Some presentations are narrowly focused; others cover a wider area. Topics included from "pure" computability theory are the computably enumerable degrees (M. Lerman), the computably enumerable sets (P. Cholak, R. Soare), definability issues in the c.e. and Turing degrees (A. Nies, R. Shore) and other degree structures (M. Arslanov, S. Badaev and S. Goncharov, P. Odifreddi, A. Sorbi). The topics involving relations between computability and other areas of logic and mathematics are reverse mathematics and proof theory (D. Cenzer and C. Jockusch, C. Chong and Y. Yang, H. Friedman and S. Simpson), set theory (R. Dougherty and A. Kechris, M. Groszek, T. Slaman) and computable mathematics and model theory (K. Ambos-Spies and A. Kucera, R. Downey and J. Remmel, S. Goncharov and B. Khoussainov, J. Knight, M. Peretyat'kin, A. Shlapentokh).
| Author | : Computability Theory and Applications AMS-IMS-SIAM Joint Summer Research Conference |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2000 |
| Genre | : Computable functions |
| ISBN | : |
Download Computability Theory and Its Applications Book in PDF, ePub and Kindle
| Author | : Robert I. Soare |
| Publisher | : Springer |
| Total Pages | : 289 |
| Release | : 2016-06-20 |
| Genre | : Computers |
| ISBN | : 3642319335 |
Download Turing Computability Book in PDF, ePub and Kindle
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.
| Author | : Steven Homer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 310 |
| Release | : 2011-12-09 |
| Genre | : Computers |
| ISBN | : 1461406811 |
Download Computability and Complexity Theory Book in PDF, ePub and Kindle
This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable. Substantial new content in this edition includes: a chapter on nonuniformity studying Boolean circuits, advice classes and the important result of Karp─Lipton. a chapter studying properties of the fundamental probabilistic complexity classes a study of the alternating Turing machine and uniform circuit classes. an introduction of counting classes, proving the famous results of Valiant and Vazirani and of Toda a thorough treatment of the proof that IP is identical to PSPACE With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool. Topics and features: Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner Provides key mathematical background information, including sections on logic and number theory and algebra Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes
| Author | : Paul E. Dunne |
| Publisher | : Prentice Hall |
| Total Pages | : 168 |
| Release | : 1991 |
| Genre | : Computers |
| ISBN | : |
Download Computability Theory Book in PDF, ePub and Kindle
A review of computability theory which determines problems that cannot be solved by existing computer programs. The book concentrates on the presentation of basic concepts as opposed to the formal mathematical aspects.
| Author | : Elaine Rich |
| Publisher | : Prentice Hall |
| Total Pages | : 1120 |
| Release | : 2008 |
| Genre | : Computers |
| ISBN | : 0132288060 |
Download Automata, Computability and Complexity Book in PDF, ePub and Kindle
For upper level courses on Automata. Combining classic theory with unique applications, this crisp narrative is supported by abundant examples and clarifies key concepts by introducing important uses of techniques in real systems. Broad-ranging coverage allows instructors to easily customise course material to fit their unique requirements.
| Author | : John Longley |
| Publisher | : Springer |
| Total Pages | : 587 |
| Release | : 2015-11-06 |
| Genre | : Computers |
| ISBN | : 3662479923 |
Download Higher-Order Computability Book in PDF, ePub and Kindle
This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages. In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them. The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers
| Author | : Rodney G. Downey |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 883 |
| Release | : 2010-10-29 |
| Genre | : Computers |
| ISBN | : 0387684417 |
Download Algorithmic Randomness and Complexity Book in PDF, ePub and Kindle
Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.
| Author | : S. Barry Cooper |
| Publisher | : CRC Press |
| Total Pages | : 428 |
| Release | : 2017-09-06 |
| Genre | : Mathematics |
| ISBN | : 1351991965 |
Download Computability Theory Book in PDF, ePub and Kindle
Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.
| Author | : S. Barry Cooper |
| Publisher | : Springer |
| Total Pages | : 292 |
| Release | : 2017-05-05 |
| Genre | : Computers |
| ISBN | : 3319436694 |
Download The Incomputable Book in PDF, ePub and Kindle
This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.
