[TYPES/announce] Book Announcement

[S B Cooper]

Book Announcement:

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NEW COMPUTATIONAL PARADIGMS -
CHANGING CONCEPTIONS OF WHAT IS COMPUTABLE

Cooper, S. Barry; Loewe, Benedikt; Sorbi, Andrea (Eds.)
2008, Springer Mathematics of Computing series XIII,
560 pp. 19 illus., Hardcover
ISBN: 978-0-387-36033-1

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 deep interconnection between 
"computation" and "proof" has originated much of the most significant work 
in constructive mathematics, theoretical computer science and mathematical 
logic of the last 70 years. Moreover, the increasingly compelling 
necessity to deal with computability in the real world (such as computing 
on continuous data, biological computing, and physical models) has brought 
focus to new paradigms of computation that are based on biological and 
physical models. These models address questions of efficiency in a 
radically new way and even threaten to move the so-called Turing barrier, 
i.e. the line between the decidable and the undecidable.

This book examines new developments in the theory and practice of 
computation from a mathematical perspective, with topics ranging from 
classical computability to complexity, from biocomputing to quantum 
computing. The book opens with an introduction by Andrew Hodges, the 
Turing biographer, who analyzes the pioneering work that anticipated 
recent developments concerning computation's allegedly new paradigms. The 
remaining material covers traditional topics in computability theory such 
as relative computability, theory of numberings, and domain theory, in 
addition to topics on the relationships between proof theory, 
computability, and complexity theory. New paradigms of computation arising 
from biology and quantum physics are also discussed, as well as the 
computability of the real numbers and its related issues. 
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