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 to 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 even challenge assumptions about the
so-called Turing barrier.
This book addresses various aspects of the ways computability and theoretical
computer science enable scientists and philosophers to deal with
mathematical and real world issues, ranging through problems related to
logic, mathematics, physical processes, real computation and learning theory.
At the same time it focuses on different ways in which computability
emerges from the real world, and how this affects our way of thinking about
everyday computational issues.
But the title Computability in Context has been carefully chosen.
The contributions to be found here are not strictly speaking ‘applied
computability’. The literature directly addressing everyday computational
questions has grown hugely since the days of Turing and the computer
pioneers. The Computability in Europe conference series and association is
built on the recognition of the complementary role that mathematics and
fundamental science plays in progressing practical work; and, at the same
time, of the vital importance of a sense of context of basic research. This
book positions itself at the interface between applied and fundamental research,
prioritising mathematical approaches to computational barriers.