Logical Approaches to Computational Barriers: CiE 2006

Abstract

The 12 papers in this special issue arose from the conference CiE 2006: Logical Approaches to Computational Barriers, held at the University of Wales Swansea in July, 2006. CiE 2006 was the second of a new series of conferences associated with the interdisciplinary network Computability in Europe. Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical development and applications. Among the aims of the network is to advance our theoretical understanding of what can and cannot be computed, by any means of computation. Its scientific vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs and machines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory or relativity. Computations may be very general, depending upon the foundations of set theory; or very specific, using the combinatorics of finite structures. CiE also works on subjects intimately related to computation, especially theories of data and information, and methods for formal reasoning about computations. The sources of new ideas and methods include practical developments in areas such as neural networks, quantum computation, natural computation, molecular computation, computational learning. Applications are everywhere, especially, in algebra, analysis and geometry, or data types and programming.