Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computabil

An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences,

This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisci

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Logical concepts and methods are of growing importance in many areas of computer science. The proofs-as-programs paradigm and the wide acceptance of Prolog show