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

A collection of essays celebrating the influence of Alan Turing's work in logic, computer science and related areas.

Rod Downey (Edited by)

9781107043480, Cambridge University Press

Hardback, published 1 May 2014

539 pages
23.5 x 15.8 x 3 cm, 0.97 kg

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.

Turing's legacy: developments from Turing's ideas in logic Rod Downey
1. Computability and analysis: the legacy of Alan Turing Jeremy Avigad and Vasco Brattka
2. Alan Turing and the other theory of computation (expanded) Lenore Blum
3. Turing in Quantumland Harry Buhrman
4. Computability theory, algorithmic randomness and Turing's anticipation Rod Downey
5. Computable model theory Ekaterina B. Fokina, Valentina Harizanov and Alexander Melnikov
6. Towards common-sense reasoning via conditional simulation: legacies of Turing in artificial intelligence Cameron E. Freer, Daniel M. Roy and Joshua B. Tenenbaum
7. Mathematics in the age of the Turing machine Thomas C. Hales
8. Turing and the development of computational complexity Steven Homer and Alan L. Selman
9. Turing machines to word problems Charles F. Miller, III
10. Musings on Turing's thesis Anil Nerode
11. Higher generalizations of the Turing model Dag Normann
12. Step by recursive step: Church's analysis of effective calculability Wilfried Sieg
13. Turing and the discovery of computability Robert Irving Soare
14. Transfinite machine models P. D. Welch.

Subject Areas: Artificial intelligence [UYQ], Computer architecture & logic design [UYF], Computer programming / software development [UM], History of mathematics [PBX], Mathematical logic [PBCD], Coding theory & cryptology [GPJ]