Classical and New Paradigms of Computation and their Complexity Hierarchies: Papers of the conference "Foundations of the Formal Sciences III" (Trends in Logic, 23)

"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."--Jacket 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

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.

Logic is famous for what Hofstadter calls limitative theorems: Gödel's incompleteness theorems, Tarski's result on the undefinability of truth, and Turing's proof of the non-computability of the halting problem.