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El. knyga: On the Foundations of Computing

(Associate Professor of Logic, University of Milan, Italy)
  • Formatas: 448 pages
  • Išleidimo metai: 19-Nov-2019
  • Leidėjas: Oxford University Press
  • Kalba: eng
  • ISBN-13: 9780192572646
Kitos knygos pagal šią temą:
  • Formatas: 448 pages
  • Išleidimo metai: 19-Nov-2019
  • Leidėjas: Oxford University Press
  • Kalba: eng
  • ISBN-13: 9780192572646
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Computing, today more than ever before, is a multi-faceted discipline which collates several methodologies, areas of interest, and approaches: mathematics, engineering, programming, and applications. Given its enormous impact on everyday life, it is essential that its debated origins are understood, and that its different foundations are explained. On the Foundations of Computing offers a comprehensive and critical overview of the birth and evolution of computing, and it presents some of the most important technical results and philosophical problems of the discipline, combining both historical and systematic analyses.

The debates this text surveys are among the latest and most urgent ones: the crisis of foundations in mathematics and the birth of the decision problem, the nature of algorithms, the debates on computational artefacts and malfunctioning, and the analysis of computational experiments. By covering these topics, On the Foundations of Computing provides a much-needed resource to contextualize these foundational issues.

For practitioners, researchers, and students alike, a historical and philosophical approach such as what this volume offers becomes essential to understand the past of the discipline and to figure out the challenges of its future.

Recenzijos

All these topics are analysed from a historical as well as a logical and epistemological point of view which makes the book a complete introduction to the philosophy of computer science. * Nicola Angius, Axiomathes * The author of this book argues that computing has three main foundations, which are mathematical foundations, engineering foundations and experimental foundations. On less than 300 pages, surprisingly broad knowledge of these three areas is presented in the three main chapters... The book can be used as a guide for a course in theoretical computer science. * Gudula Rünger, zbMATH Open * For practitioners, researchers, and students alike, a historical and philosophical approach such as what this volume offers becomes essential to understand the past of the discipline and to gure out the challenges of its future. * MathSciNet *

1 Introduction
1(4)
Part I The Mathematical Foundation
5(110)
2 A Fundamental Crisis
7(14)
2.1 The Foundations of Mathematics Debated
7(1)
2.2 Logical Roots
8(2)
2.3 Logicism
10(5)
2.4 Finitism
15(2)
2.5 Intuitionism
17(4)
Exercises
19(2)
3 Computing and Deciding
21(10)
3.1 Enumerability
21(3)
3.2 Encoding
24(1)
3.3 Diagonalization
25(2)
3.4 The Decision Problem
27(4)
Exercises
28(3)
4 What is Computable?
31(12)
4.1 Mathematical Induction
31(3)
4.2 Primitive Recursion
34(2)
4.3 Partial Recursion
36(2)
4.4 Church's Thesis
38(5)
Exercises
40(3)
5 Mechanical Computation
43(22)
5.1 Turing Computability
43(8)
5.2 The Universal Machine
51(3)
5.3 The Halting Problem
54(2)
5.4 Turing's Thesis
56(9)
Exercises
63(2)
6 On the Nature of Algorithms
65(16)
6.1 Fast Backwards
65(4)
6.2 Intuitive Explanation
69(3)
6.3 Algorithms as Specifications
72(1)
6.4 Algorithms as Procedures
73(1)
6.5 Algorithms as Abstract Machines
74(2)
6.6 Equivalent Algorithms
76(5)
Exercises
80(1)
7 Computing as a Mathematical Discipline
81(34)
7.1 Proofs as Programs
81(7)
7.2 Program Correctness
88(12)
7.3 The Debate
100(7)
7.4 Formal Computational Validity
107(8)
Exercises
114(1)
Part II The Engineering Foundation
115(100)
8 The First Generation of Computers
117(26)
8.1 Shannon's Circuits
117(5)
8.2 Early Memories
122(8)
8.3 Von Neumann Design
130(6)
8.4 Universality and All-purposefulness
136(7)
Exercises
140(3)
9 The Laws of Evolution
143(28)
9.1 Computing grows
143(1)
9.2 New Memories
144(7)
9.3 Miniaturization, Parallelism, and Compatibility
151(5)
9.4 The First Law
156(5)
9.5 Computational Growth
161(10)
Exercises
170(1)
10 Properties of Implemented Computations
171(18)
10.1 Physical Computing
171(5)
10.2 Functionality
176(5)
10.3 Usability
181(3)
10.4 Efficiency
184(2)
10.5 Limits of the Church-Turing Thesis
186(3)
Exercises
187(2)
11 Specification and Implementation
189(10)
11.1 The Debate on Implementation
189(4)
11.2 Correct Implementations
193(3)
11.3 Miscomputation
196(3)
Exercises
198(1)
12 Computing as an Engineering Discipline
199(16)
12.1 Software Engineering
199(7)
12.2 The Debate
206(3)
12.3 Physical Computational Validity
209(6)
Exercises
213(2)
Part III The Experimental Foundation
215(58)
13 Elements of Experimental Computing
217(14)
13.1 Experimental Computer Science
217(5)
13.2 On Computational Hypotheses
222(4)
13.3 On Computational Experiments
226(5)
Exercises
230(1)
14 Models and Simulations
231(10)
14.1 On Models
231(4)
14.2 On Computer Simulations
235(3)
14.3 Epistemic Role of Computer Simulations
238(3)
Exercises
240(1)
15 Formal Relations
241(14)
15.1 Identity and Dependence
241(3)
15.2 Isomorphism
244(2)
15.3 Analogy and Similarity
246(2)
15.4 Variants of Simulationism
248(7)
Exercises
254(1)
16 Computing as an Experimental Discipline
255(16)
16.1 A Balanced Approach
255(1)
16.2 Evaluation
256(6)
16.3 Maximal Criteria: Robustness and Reliability
262(3)
16.4 Minimal Criteria: Usability and Fitness
265(2)
16.5 Experimental Computational Validity
267(4)
Exercises
269(2)
17 Conclusion
271(2)
Bibliography 273(20)
Index 293
Giuseppe Primiero is Associate Professor of Logic at the Department of Philosophy, University of Milan (Italy). He acts as President of the DHST Commission for the History and Philosophy of Computing (HaPoC) and Secretary General of the Association Computability in Europe (CiE). His research interests are primarily in Logic and Computation, Philosophy of Computing and Information.