The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies.
This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.
Author(s): Benedikt Löwe, Boris Piwinger, Thoralf Räsch (eds.)
Series: Trends in Logic 23
Publisher: Springer
Year: 2004
Language: English
Pages: 265
Tags: Computer Science, general; Theory of Computation; Mathematical Logic and Foundations; Math Applications in Computer Science; Mathematics of Computing; Algorithms
Front Matter....Pages i-xiii
Complexity hierarchies derived from reduction functions....Pages 1-14
Quantum query algorithms and lower bounds....Pages 15-32
Algebras of minimal rank: overview and recent developments....Pages 33-46
Recent developments in iterated forcing theory....Pages 47-60
Classification problems in algebra and topology....Pages 61-75
Using easy optimization problems to solve hard ones....Pages 77-93
On Sacks forcing and the Sacks property....Pages 95-139
Supertask computation....Pages 141-158
A refinement of Jensen's constructible hierarchy....Pages 159-169
Effective Hausdorff dimension....Pages 171-186
Axiomatizability of algebras of binary relations....Pages 187-205
Forcing axioms and projective sets of reals....Pages 207-222
Post's and other problems of supertasks of higher type....Pages 223-237
Back Matter....Pages 239-259
