New Computational Paradigms

This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective.

It covers topics ranging from classical computability to complexity, from biocomputing to quantum computing. The book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book. In recent years, classical computability has expanded beyond its original scope to address issues related to computability and complexity in algebra, analysis, and physics. The book opens with an introduction by Alan Hodges, the Turing biographer, who analyzes the pioneering work that anticipated recent developments concerning computation's allegedly new paradigms.

Explores new developments in the theory and practice of computation from a mathematical perspective Includes topics ranging from classical computability to complexity, biocomputing, and quantum computing Offers content that appeals to specialists and non-specialists alike Features contributors who are prominent scholars and internationally known specialists Includes supplementary material: sn.pub/extras

Inhalt
The Turing Model of Computation and its Applications to Logic, Mathematics, Philosophy, and Computer Science.- Alan Turing, Logical and Physical.- Computability and Numberings.- Computation as Conversation.- Computation Paradigms in Light of Hilbert's Tenth Problem.- Elementary Algorithms and Their Implementations.- Applications of the KleeneKreisel Density Theorem to Theoretical Computer Science.- Church Without Dogma: Axioms for Computability.- Computability on Topological Spaces via Domain Representations.- On the Power of Broadcasting in Mobile Computing.- Logic, Algorithms and Complexity.- The Computational Power of Bounded Arithmetic from the Predicative Viewpoint.- Effective Uniform Bounds from Proofs in Abstract Functional Analysis.- Effective Fractal Dimension in Algorithmic Information Theory.- Metamathematical Properties of Intuitionistic Set Theories with Choice Principles.- New Developments in Proofs and Computations.- Models of Computation from Nature.- From Cells to (Silicon) Computers, and Back.- Computer Science, Informatics, and Natural ComputingPersonal Reflections.- Computable Analysis and Real Computation.- A Survey on Continuous Time Computations.- A Tutorial on Computable Analysis.- A Continuous Derivative for Real-Valued Functions.- Infinite Time Computable Model Theory.