COMPUTABILITY AND UNSOLVABILITY DOVER BOOKS ON COMPUTER SCIENCE

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Computability And Unsolvability

Author : Martin Davis
ISBN : 9780486151069
Genre : Mathematics
File Size : 52.86 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

Business Research Methodology With Cd

Author : Srivastava
ISBN : 9781259081903
Genre : Business
File Size : 80.6 MB
Format : PDF
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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: Business

The Undecidable

Author : Martin Davis
ISBN : 0486432289
Genre : Mathematics
File Size : 63.69 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

Applied Nonstandard Analysis

Author : Martin Davis
ISBN : 9780486152349
Genre : Mathematics
File Size : 77.19 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

The Universal Computer

Author : Martin Davis
ISBN : 9781351384810
Genre : Mathematics
File Size : 72.57 MB
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The breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. Written by Martin Davis, respected logician and researcher in the theory of computation, The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ideas, and discoveries of seven remarkable mathematicians. It tells the stories of the unsung heroes of the computer age – the logicians.
Category: Mathematics

Three Views Of Logic

Author : Donald W. Loveland
ISBN : 9781400848751
Genre : Mathematics
File Size : 21.70 MB
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Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses
Category: Mathematics

Logic For Computer Science

Author : Jean H. Gallier
ISBN : 9780486780825
Genre : Computers
File Size : 85.85 MB
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This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.
Category: Computers

A First Course In Functional Analysis

Author : Martin Davis
ISBN : 9780486315812
Genre : Mathematics
File Size : 58.16 MB
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Designed for undergraduate mathematics majors, this self-contained exposition of Gelfand's proof of Wiener's theorem explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and more. 1966 edition.
Category: Mathematics

On Formally Undecidable Propositions Of Principia Mathematica And Related Systems

Author : Kurt Gödel
ISBN : 9780486158402
Genre : Mathematics
File Size : 55.64 MB
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First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Category: Mathematics

Computable Functions

Author : Nikolai Konstantinovich Vereshchagin
ISBN : 9780821827321
Genre : Mathematics
File Size : 57.25 MB
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This lively and concise book is based on the lectures for undergraduates given by the authors at the Moscow State University Mathematics Department and covers the basic notions of the general theory of computation. It begins with the definition of a computable function and an algorithm and discusses decidability, enumerability, universal functions, numberings and their properties, $m$-completeness, the fixed point theorem, arithmetical hierarchy, oracle computations, and degrees of unsolvability. The authors also cover specific computational models, such as Turing machines and recursive functions. The intended audience includes undergraduate students majoring in mathematics or computer science, and all mathematicians and programmers who would like to learn the basics of the general theory of computation.
Category: Mathematics