Löwe B., Piwinger B., Räsch T. (eds.) Classical and New Paradigms of Computation and their Complexity Hierarchies

Papers of the conference Foundations of the Formal Sciences III. — Berlin: Springer, 2004. — 265 p.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.Complexity hierarchies derived from reduction functions
Quantum query algorithms and lower bounds
Algebras of minimal rank: overview and recent developments
Recent developments in iterated forcing theory
Classification problems in algebra and topology
Using easy optimization problems to solve hard ones
On Sacks forcing and the Sacks property
Supertask computation
A refinement of Jensen's constructible hierarchy
Effective Hausdorff dimension
Axiomatizability of algebras of binary relations
Forcing axioms and projective sets of reals
Post's and other problems of supertasks of higher type