The Universal Turing Machine
A Half-Century Survey
1st Edition
Published on 15. August 1991
Book
Paperback/Softback
676 pages
978-0-19-853774-8 (ISBN)
Description
This volume commemorates the work of Alan Turing, because it was Turing who not only introduced the most persuasive and influential concept of a machine model of effective computability but who also anticipated in his work the diversity of topics brought together here. As Newman put it in his memoir of Turing, "The central problem with which he started and to which he constantly returned is the extent and the limitations of mechanistic explanations of nature."
Turing's paper "On computable numbers, with an application to the Entscheidungs problem" appeared in print in 1937. It contained Turing's thesis that every `effective' computation can be programmed on a Turing machine. Furthermore it contained the unsolvability of the halting problem and of the decision problem for first-order logic, and it presented the invention of the universal Turing machine. The publication of this idea is acknowledged as a landmark of the computer age.
Part I of the volume explores the historical aspect with essays on the background, on Turing's work, and on subsequent developments. Part II contains an extensive series of essays on the influence and applications of these ideas in mathematics, mathematical logic, philosophy of mathematics, computer science, artificial intelligence, philosophy of language, philosophy of mind, and physics.
Turing's paper "On computable numbers, with an application to the Entscheidungs problem" appeared in print in 1937. It contained Turing's thesis that every `effective' computation can be programmed on a Turing machine. Furthermore it contained the unsolvability of the halting problem and of the decision problem for first-order logic, and it presented the invention of the universal Turing machine. The publication of this idea is acknowledged as a landmark of the computer age.
Part I of the volume explores the historical aspect with essays on the background, on Turing's work, and on subsequent developments. Part II contains an extensive series of essays on the influence and applications of these ideas in mathematics, mathematical logic, philosophy of mathematics, computer science, artificial intelligence, philosophy of language, philosophy of mind, and physics.
Reviews / Votes
'... a fitting tribute to one of the most influential figures in mathematical logic and computer science.' Journal of Logic and Computation 'a generally well-written account of Turing's work which manages to convey the broad scope of his influence on later developments in mathematical logic, computer science, and artificial intelligence. I would recommend the book to anyone who has an interest in computability theory or mathematical logic and its applications in computer science... One of the great merits of the book is that it is relatively self-contained and the material is largely expository and consequently the book will also attract the lay reader who is interested in the development of mathematical ideas... this collection is to be welcomed as a fitting tribute to the work of one of the most influential figures in mathematical logic and computer science.' Journal of Logic and ComputationMore details
Language
English
Place of publication
Oxford
United Kingdom
Target group
College/higher education
Professional and scholarly
Illustrations
line figures throughout
Dimensions
Height: 236 mm
Width: 155 mm
Thickness: 37 mm
Weight
992 gr
ISBN-13
978-0-19-853774-8 (9780198537748)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Content
List of contributors; Preface; PART 1: A. Hodges: Alan Turing and the Turing Machine; S.C. Kleene: Turing's analysis of computability, and major applications of it; R. Gandy: The confluence of ideas in 1936; S. Feferman: Turing in the Land of O(z); M. Davis: Mathematical logic and the origin of modern computing. PART 2: M.A. Arbib: From universal Turing machines to self-reproduction; M.J. Beeson: Computerizing mathematics: Logic and computation; C.H. Bennett: Logical depth and physical complexity; A.H. Brady: The busy beaver game and the meaning of life; G.J. Chaitin: An algebraic equation for the halting probability; M. Conrad: The price of programmability; E. Dahlhaus & J.A. Makowsky: Gandy's principles for mechanisms as a model of parallel computation; M. Davis: Influences of mathematical logic on computer science; J.E. Fenstad: Language and computations; D. Finkelstein: Finite physics; O. Goldreich: Randomness, interactive proofs, and zero-knowledge - a survey; Y. Gurevich: Algorithms in the world of bounded resources; B. Hasslacher: Beyond the Turing machine; M. Koppel: Structure; J.A. Makowsky: Mental images and the architecture of concepts; D. Michie: The fifth generation's unbridged gap; R. Penrose: On the physics and mathematics of thought; R. Rosen: Effective processes and natural law; H. Schnelle: Turing naturalized: Von Neumann's unfinished project; U. Schoening: Complexity theory and interaction; J.C. Shepherdson: Mechanisms for computing over arbitrary structures; B.A. Trakhtenbrot: Comparing the Church and Turing approaches: two prophetical messages; O. Wiener: Form and content in thinking Turing machines; Appendix.