Computability in context. Computation and logic in the real world

Description

* The first exposition on super-recursive algorithms, systematizing all main classes and providing an accessible, focused examination of the theory and its ramifications * Demonstrates how these algorithms are more appropriate as mathematical models for modern computers and how they present a better framework for computing methods * Develops a new practically-oriented perspective on the theory of algorithms, computation, and automata, as a whole Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier. This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with m.  Read more... 1. Computation, information, and the arrow of time / P. Adriaans & P. van Emde Boas -- 2. The isomorphism conjecture for NP / M. Agrawal -- 3. 3. The Ershov hierarchy / M. M. Arslanov -- 4. Complexity and approximation in reoptimization / G. Ausiello, V. Bonifaci, & B. Escoffier -- 5. Definability in the real universe / S. B. Cooper -- 6. HF-computability / Y. L. Ershov, V. G. Puzarenko, & A. I. Stukachev -- 7. The mathematics of computing between logic and physics / G. Longo & T. Paul -- 8. Liquid state machines : Motivation, theory, and applications / W. Maass -- 9. Experiments on an internal approach to typed algorithms in analysis / D. Normann -- 10. Recursive functions : An archeological look / P. Odifreddi -- 11. Reverse mathematics and well-ordering principles / M. Rathjen & A. Weiermann -- 12. Discrete transfinite computation models / P. D. Welch