Rodney G. Downey - Böcker

The idea for this book was conceived over the second bottle of Villa Maria's Caber­ net Medot '89, at the dinner of the Australasian Combinatorics Conference held at Palmerston North, New Zealand in December 1990, where the authors first met and discovered they had a number of interests in common. Initially, we embarked on a small project to try to formulate reductions to address the apparent parame­ terized intractability of DOMINATING SET, and to introduce a structure in which to frame our answers. Having spent several months trying to get the definitions for the reductions right (they now seem so obvious), we turned to our tattered copies of Garey and Johnson's work [239]. We were stunned to find that virtually none of the classical reductions worked in the parameterized setting. We then wondered if we'd be able to find any interesting reductions. Several years, many more bottles, so many papers, and reductions later it [3] seemed that we had unwittingly stumbled upon what we believe is a truly central and new area of complexity theory. It seemed to us that the material would be of great interest to people working in areas where exact algorithms for a small range of parameters are natural and useful (e. g. , Molecular Biology, VLSI design). The tractability theory was rich with distinctive and powerful techniques. The intractability theory seemed to have a deep structure and techniques all of its own.

This book is concerned with the theory of computability and complexity over the real numbers. This theory was initiated by Turing, Grzegorczyk, Lacombe, Banach, and Mazur and has seen rapid growth in recent years. Computability and complexity theory are two central areas of research in theoretical computer science. Until recently, most work in these areas concentrated on problems over discrete structures, but there has been enormous growth of computability theory and complexity theory over the real numbers and other continuous structures, especially incorporating concepts of "randomness". One reason for this growth is that more and more computation problems over the real numbers are being dealt with by computer scientists - in computational geometry and in the modeling of dynamical and hybrid systems. Scientists working on these questions come from such diverse fields as theoretical computer science, domain theory, logic, constructive mathematics, computer arithmetic, numerical mathematics, and analysis. An essential resource for all researchers in theoretical computer science, logic, computability theory and complexity.

This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years.

This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity.

The idea for this book was conceived over the second bottle of Villa Maria's Caber­ net Medot '89, at the dinner of the Australasian Combinatorics Conference held at Palmerston North, New Zealand in December 1990, where the authors first met and discovered they had a number of interests in common.

The theory of algorithmic randomness uses tools from computability theory and algorithmic information theory to address questions such as these. It will be of interest to researchers and students in computability theory, algorithmic information theory, and theoretical computer science.

This is the first book which gives a unified theory for countable and uncountable computable structures. The work treats computable linear orderings, graphs, groups and Boolean algebras unified with computable metric and Banach spaces, profinite groups, and the like.

The 7th and the 8th Asian Logic Conferences belong to the series of logic conferences inaugurated in Singapore in 1981. This meeting is held once every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association for Symbolic Logic.This book contains papers — many of them surveys by leading experts — of both the 7th meeting (in Hsi-Tou, Taiwan) and the 8th (in Chongqing, China). The volume planned for the 7th meeting was interrupted by the earthquake in Taiwan and the decision was made to combine the two proceedings. The 8th conference is also the ICM2002 Satellite Conference on Mathematical Logic.

This volume is devoted to the main areas of mathematical logic and applications to computer science. There are articles on weakly o-minimal theories, algorithmic complexity of relations, models within the computable model theory, hierarchies of randomness tests, computable numberings, and complexity problems of minimal unsatisfiable formulas. The problems of characterization of the deduction-detachment theorem, Δ1-induction, completeness of Leśniewski's systems, and reduction calculus for the satisfiability problem are also discussed.The coverage includes the answer to Kanovei's question about the upper bound for the complexity of equivalence relations by convergence at infinity for continuous functions. The volume also gives some applications to computer science such as solving the problems of inductive interference of languages from the full collection of positive examples and some negative data, the effects of random negative data, methods of formal specification and verification on the basis of model theory and multiple-valued logics, interval fuzzy algebraic systems, the problems of information exchange among agents on the base topological structures, and the predictions provided by inductive theories.

The 10th Asian Logic Conference is part of the series of logic conferences inaugurated in Singapore in 1981. This meeting is held every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association of Symbolic Logic.This volume contains papers from the 10th meeting held in Kobe, Japan.