New Computational Paradigms: Changing Conceptions of What Is Computable

The recent necessity to deal with computability in the real world (computing on continuous data, biological computing, physical computing, etc.) has switched attention to new paradigms of computation, based on biological and physical models. This book looks at new developments in the theory and practice of computation from a mathematical and predominantly logical perspective, with topics ranging from classical computability to complexity, biocomputing and quantum computing. Traditional topics in computability theory are also covered as well as relationships between proof theory,  computability and complexity theory, new paradigms of computation arising from biology and quantum physics and issues related to computability of the real numbers. The book is addressed to researchers and graduate students in mathematics, philosophy and computer science with a special interest in logic and foundational issues. Logicians and theoretical physicists will also benefit from this book.