Rod Downey

The Moralist

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.

Developments from Turing's Ideas in Logic

Turing's Legacy

Denis R. Hirschfeldt

The book contains 8 detailed expositions of the lectures given at the Kaikoura 2000 Workshop on Computability, Complexity, and Computational Algebra. Topics covered include basic models and questions of complexity theory, the Blum-Shub-Smale model of computation, probability theory applied to algorithmics (randomized alogrithms), parametric complexity, Kolmogorov complexity of finite strings, computational group theory, counting problems, and canonical models of ZFC providing a solution to continuum hypothesis. The text addresses students in computer science or mathematics, and professionals in these areas who seek a complete, but gentle introduction to a wide range of techniques, concepts, and research horizons in the area of computational complexity in a broad sense.

Minicourses in Algorithmics, Complexity and Computational Algebra. Mathematics Workshop, Kaikoura, January 7-15, 2000

Aspects of Complexity

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

Ding Decheng

Tung Shih Ping

Qiu Yu Hui

Mariko Yasugi

The 7th and the 8th Asian Logic Conferences belong to the series of logic conferences inaugurated in Singapore in 1981. This meeting is held once every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association for Symbolic Logic. This book contains papers — many of them surveys by leading experts — of both the 7th meeting (in Hsi-Tou, Taiwan) and the 8th (in Chongqing, China). The volume planned for the 7th meeting was interrupted by the earthquake in Taiwan and the decision was made to combine the two proceedings. The 8th conference is also the ICM2002 Satellite Conference on Mathematical Logic. Contents:Five Puzzles about Mathematics in Search of Solutions (C S Chihara)Computability, Definability and Algebraic Structures (R Downey)Popper and Miller, and Induction and Deduction (E Eells)Enlargements of Polynomial Coalgebras (R Goldblatt)A Common Structure of Logical and Algebraic Algorithms (Y Kawaguchi)Computational Complexity of Fractals (K I Ko)Definability in Local Degree Structures — A Survey of Recent Results Related to Jump Classes (A Li & Y Yang)An Application of NDJPROP to the Catch and Throw Mechanism (M Nakata et al.)A Problem on Theories with a Finite Number of Countable Models (A Tsuboi)Diamond Embeddings into the D.C.E. Degrees with 0 and 1 Preserved (G Wu)and other papers Readership: Logicians, computer scientists, research mathematicians and graduate students. Keywords:

Rod Downey

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