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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.
Professor Rod Downey, School of Mathematics and Computer Sciences, Victoria University, Wellington, New Zealand.
Professor Denis Hirschfeldt, School of Mathematics and Computer Sciences, Victoria University, Wellington, New Zealand.
E. Allender and C. McCartin, Basic Complexity · F. Cucker, Real Computation · P. Diaconis, Randomized Algorithms · M. Fellows, Parameterized Complexity: New Developments and Research Frontiers · L. Fortnow, Kolmogorov Complexity · A. Niemeyer and C. Praeger, Complexity and Computation in Matrix Groups · D. Welsh and A. Gale, The Complexity of Counting Problems · H. Woodin, The Ω Conjecture.