COMPUTABILITY AND UNSOLVABILITY DOVER BOOKS ON COMPUTER SCIENCE

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Computability And Unsolvability

Author : Martin Davis
ISBN : 9780486151069
Genre : Mathematics
File Size : 50.25 MB
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Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.
Category: Mathematics

The Undecidable

Author : Martin Davis
ISBN : 0486432289
Genre : Mathematics
File Size : 54.46 MB
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"A valuable collection both for original source material as well as historical formulations of current problems." — The Review of Metaphysics "Much more than a mere collection of papers. A valuable addition to the literature." — Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field , this classic reference is ideally suited as a text for graduate and undergraduate courses in logic, philosophy, and foundations of mathematics. It is also appropriate for self-study. The text opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Supplementary items include corrections, emendations, and added commentaries by Godel, Church, and Kleene for this volume's original publication, along with a helpful commentary by the editor.
Category: Mathematics

The Foundations Of Computability Theory

Author : Borut Robič
ISBN : 9783662448083
Genre : Computers
File Size : 87.28 MB
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This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.
Category: Computers

Meilensteine Der Rechentechnik

Author : Herbert Bruderer
ISBN : 9783110397895
Genre : Computers
File Size : 84.3 MB
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This book presents key milestones in the history of computer technology and the early days of computer science. A focus is placed on the new devices and research findings that have aroused particular attention in past years. Many tables provide a global overview on the earliest digital computers. A multilingual bibliography with over 3,000 titles completes the volume.
Category: Computers

Computability Theory

Author : S. Barry Cooper
ISBN : 1584882379
Genre : Mathematics
File Size : 65.54 MB
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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.
Category: Mathematics

Applied Nonstandard Analysis

Author : Martin Davis
ISBN : 9780486152349
Genre : Mathematics
File Size : 45.97 MB
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This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.
Category: Mathematics

Interactive Fortran 77

Author : Ian David Chivers
ISBN : STANFORD:36105033207262
Genre : Computers
File Size : 76.92 MB
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Category: Computers

An Introduction To Mathematical Logic

Author : Richard E. Hodel
ISBN : 9780486497853
Genre : Mathematics
File Size : 35.61 MB
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This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
Category: Mathematics

Der Turing Omnibus

Author : A.K. Dewdney
ISBN : 9783642788727
Genre : Computers
File Size : 38.61 MB
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Der Turing Omnibus macht in 66 exzellent geschriebenen Beiträgen Station bei den interessantesten Themen aus der Informatik, der Computertechnologie und ihren Anwendungen.
Category: Computers

Casys

Author : Daniel M. Dubois
ISBN : 2960026217
Genre : Self-organizing systems
File Size : 72.7 MB
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Category: Self-organizing systems