Turing's Legacy: Developments from Turing's Ideas in Logic

doi:10.1017/CBO9781107338579

Alan Turing was an inspirational figure who is now recognised as a genius of modern mathematics. In addition to leading the Allied forces' code-breaking effort at Bletchley Park in World War II, he proposed the theoretical foundations of modern computing and anticipated developments in areas from information theory to computer chess. His ideas have been extraordinarily influential in modern mathematics and this book traces such developments by bringing together essays by leading experts in logic, artificial intelligence, computability theory and related areas. Together, they give insight into this fascinating man, the development of modern logic, and the history of ideas. The articles within cover a diverse selection of topics, such as the development of formal proof, differing views on the Church–Turing thesis, the development of combinatorial group theory, and Turing's work on randomness which foresaw the ideas of algorithmic randomness that would emerge many years later.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Turing's legacy: developments from Turing's ideas in logic
pp vii-x
- By Rod Downey, Victoria University of Wellington
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Computability and analysis: the legacy of Alan Turing
pp 1-47
- By Jeremy Avigad, Carnegie Mellon University, Vasco Brattka, University of Cape Town
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Alan Turing and the other theory of computation (expanded)
pp 48-69
- By Lenore Blum, Carnegie Mellon University
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Turing in Quantumland
pp 70-89
- By Harry Buhrman, University of Amsterdam
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Computability theory, algorithmic randomness and Turing's anticipation
pp 90-123
- By Rod Downey, Victoria University of Wellington
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Computable model theory
pp 124-194
- By Ekaterina B. Fokina, University of Vienna, Valentina Harizanov, George Washington University, Alexander Melnikov, Victoria University of Wellington
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Towards common-sense reasoning via conditional simulation: legacies of Turing in Artificial Intelligence
pp 195-252
- By Cameron E. Freer, Massachusetts Institute of Technology, Daniel M. Roy, University of Cambridge, Joshua B. Tenenbaum, Massachusetts Institute of Technology
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Mathematics in the age of the Turing machine
pp 253-298
- By Thomas C. Hales, University of Pittsburgh
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Turing and the development of computational complexity
pp 299-328
- By Steven Homer, Boston University, Alan L. Selman, State University of New York
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Turing machines to word problems
pp 329-385
- By Charles F. Miller, University of Melbourne
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Musings on Turing's Thesis
pp 386-396
- By Anil Nerode, Cornell University
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Higher generalizations of the Turing Model
pp 397-433
- By Dag Normann, The University of Oslo
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Step by recursive step: Church's analysis of effective calculability
pp 434-466
- By Wilfried Sieg, Carnegie Mellon University
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Turing and the discovery of computability
pp 467-492
- By Robert Irving Soare, The University of Chicago
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Transfinite machine models
pp 493-529
- By P.D. Welch, University of Bristol
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Turing's Legacy

Developments from Turing's Ideas in Logic

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Turing's legacy: developments from Turing's ideas in logic
pp vii-x

Computability and analysis: the legacy of Alan Turing
pp 1-47

Alan Turing and the other theory of computation (expanded)
pp 48-69

Turing in Quantumland
pp 70-89

Computability theory, algorithmic randomness and Turing's anticipation
pp 90-123

Computable model theory
pp 124-194

Towards common-sense reasoning via conditional simulation: legacies of Turing in Artificial Intelligence
pp 195-252

Mathematics in the age of the Turing machine
pp 253-298

Turing and the development of computational complexity
pp 299-328

Turing machines to word problems
pp 329-385

Musings on Turing's Thesis
pp 386-396

Higher generalizations of the Turing Model
pp 397-433

Step by recursive step: Church's analysis of effective calculability
pp 434-466

Turing and the discovery of computability
pp 467-492

Transfinite machine models
pp 493-529

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Turing's Legacy

Developments from Turing's Ideas in Logic

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