![]() ![]() His main research interests lie in algebra, logic and complexity theory. rod downey is Professor of Mathematics at Victoria University of Wellington, New Zealand. 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. Together, they give insight into this fascinating man, the development of modern logic, and the history of ideas. 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. In addition to being a leading participant in the Allied forces’ codebreaking 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. Turing’s Legacy: Developments from Turing’s Ideas in Logic Alan Turing was an inspirational figure who is now recognized as a genius of modern mathematics. Turing and the discovery of computability Robert Irving Soareġ4. Step by recursive step: Church's analysis of effective calculability Wilfried Siegġ3. Higher generalizations of the Turing model Dag Normannġ2. Musings on Turing's thesis Anil Nerodeġ1. Turing machines to word problems Charles F. Turing and the development of computational complexity Steven Homer and Alan L. ![]() Mathematics in the age of the Turing machine Thomas C. Towards common-sense reasoning via conditional simulation: legacies of Turing in artificial intelligence Cameron E. Fokina, Valentina Harizanov and Alexander MelnikovĦ. Computability theory, algorithmic randomness and Turing's anticipation Rod Downeyĥ. Alan Turing and the other theory of computation (expanded) Lenore BlumĤ. ![]() Computability and analysis: the legacy of Alan Turing Jeremy Avigad and Vasco BrattkaĢ. Content: Turing's legacy: developments from Turing's ideas in logic Rod Downeyġ. ![]()
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