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, arising from the conference "Computability in Europe 2007:
Computation and Logic in the Real World", addresses various aspects of the ways computability 
and theoretical computer science enable scientists and philosophers to deal with mathematical 
and real-world issues, covering problems related to logic, mathematics, physical processes, real
computation and learning theory. At the same time it will focus on different ways in which 
computability emerges from the real world, and how this affects our way of thinking about everyday
computational issues.

Contents:

* Computation, Information, and the Arrow of Time (P Adriaans & P van Emde
Boas)
* The Isomorphism Conjecture for NP (M Agrawal)
* The Ershov Hierarchy (M M Arslanov)
* Complexity and Approximation in Reoptimization (G Ausiello et al.)
* Definability in the Real Universe (S B Cooper)
* HF-Computability (Y L Ershov et al.)
* The Mathematics of Computing Between Logic and Physics (G Longo & T
Paul)
* Liquid State Machines: Motivation, Theory, and Applications (W Maass)
* Experiments on an Internal Approach to Typed Algorithms in Analysis (D
Normann)
* Recursive Functions: An Archeological Look (P Odifreddi)
* Reverse Mathematics and Well-Ordering Principles (M Rathjen & A
Weiermann)
* Discrete Transfinite Computation Models (P D Welch)

ISBN:   978-1-84816-245-7, 1-84816-245-6
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