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首页永恒的图灵:20位科学家对图灵思想的解构与超越英文版
永恒的图灵:20位科学家对图灵思想的解构与超越 作者简介 · · · · · · S. 巴里·库珀(S. Barry Cooper) 本书付梓前不幸逝世。生前为利兹大学数理逻辑教授,欧洲“可计算性学会”主席,“图灵百年委员会”主席。他主编的《Alan Turing:His Work and Impact》一书曾荣获2013年美国专业与学术杰出出版奖 安德鲁·霍奇斯(Andrew Hodges) 牛津大学数学研究所教授、高级研究员。他撰写了畅销全球的权威图灵传记《Alan Turing:The Enigma》,此书也是奥斯卡获奖影片《模仿游戏》的文学原本。
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THE ONCE AND FUTURE TURING:
COMPUTING THE WORLD
Alan Turing (1912–1954) made seminal contributionstomathematicallogic,computation,
computer science, artificial intelligence, cryptography and theoretical biology.
In this volume, outstanding scientific thinkers take a fresh look at the great range of
Turing’s contributions, on how the subjects have developed since his time, and how they
might develop still further.
Thesespeciallycommissionedessays willprovokeandengross thereader whowishes to
understandbetterthe lastingsignificanceof oneofthe twentiethcentury’s deepestthinkers.
Until his death in 2015,
S. BARRY COOPER was Professor of Mathematical Logic at
theUniversityof Leeds.Hewas botha leadingfigurein thetheoryof Turingcomputability,
and a noted advocate of multidisciplinary research, especially in connection with the
theoreticalandpracticallimitsofthecomputable.AsPresident ofComputabilityinEurope,
he was responsible for many international conferences. He chaired the Turing Centenary
Committee, and edited the prize-winning critical edition of Turing’s publications: Alan
Turing – His Work and Impact.
ANDREW HODGES is a Senior Research Fellow at the Mathematical Institute,
University of Oxford. Hismainresearch is in fundamental physics, asacolleagueof Roger
Penrose, but he is also the biographer of Alan Turing. His book Alan Turing: The Enigma
(1983) has reached a wide audience and has inspired works of drama, music, art and film.

University Printing House, Cambridge CB2 8BS, United Kingdom
Cambridge University Press is part of the University of Cambridge.
It furthers the University’s mission by disseminating knowledge in the pursuit of
education, learning and research at the highest international levels of excellence.
www.cambridge.org
Information on this title: www.cambridge.org/9781107010833
c
Cambridge University Press 2016
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2016
Printed in the United Kingdom by Clays, St Ives plc
A catalogue record for this publication is available from the British Library
ISBN 978-1-107-01083-3 Hardback
Cambridge University Press has no responsibility for the persistence or accuracy
of URLs for external or third-party internet websites referred to in this publication,
and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.

Contents
Contributors page ix
Preface xi
Introduction xiii
Part One: Inside Our Computable World, and the Mathematics of Uni-
versality 1
1 Algorithms, Equations, and Logic 4
Martin Davis
References 18
2 The Forgotten Turing 20
J.M.E. Hyland
References 32
3 Turing and the Primes 34
Andrew R. Booker
References 52
4 Cryptography and Computation after Turing 53
Ueli Maurer
4.1 Introduction 54
4.2 Cryptography 55
4.3 Computation 57
4.4 The Diffie–Hellman key-agreement protocol 58
4.5 Discrete logarithms and other computational problems on
groups 62
4.6 Discrete logarithm algorithms 63
4.7 Abstract models of computation 66
4.8 Proving security: lower bounds for complexity 68
4.9 Conclusions 75
References 76
v
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