This textbook discusses the most fundamental and puzzling questions about the foundations of computing. In 23 lecture-sized chapters it provides an exciting tour through the most important results in the field of computability and time complexity, including the Halting Problem, Rice's Theorem, Kleene's Recursion Theorem, the Church-Turing Thesis, Hierarchy Theorems, and Cook-Levin's Theorem. Each chapter contains classroom-tested material, including examples and exercises. Links between adjacent chapters provide a coherent narrative. Fundamental results are explained lucidly by means of programs written in a simple, high-level imperative programming language, which only requires basic mathematical knowledge. Throughout the book, the impact of the presented results on the entire field of computer science is emphasised. Examples range from program analysis to networking, from database programming to popular games and puzzles. Numerous biographical footnotes about the famous scientists who developed the subject are also included. "Limits of Computation" offers a thorough, yet accessible, introduction to computability and complexity for the computer science student of the 21st century.

Illustrates proofs by means of programs written in a high-level imperative programming language Includes chapters on the emergent fields of molecular and quantum computing Highlights countless connections to all areas in computer science Includes supplementary material: sn.pub/extras

Autorentext

Dr. Bernhard Reus is a Senior Lecturer in the Department of Informatics at the University of Sussex, with 15 years experience in teaching computability and complexity.

Inhalt

Foreword.- Limits? What Limits?.- Part I Computability.- Problems and Effective Procedures.- The WHILE-Language.- Semantics of WHILE.- Extensions of WHILE.- Programs As Data Objects.- A Self-Interpreter for WHILE.- An Undecidable (Non-computable) Problem.- More Undecidable Problems.- Self-referencing Programs.- The Church-Turing Thesis.- Part II Complexity.- Measuring Time Usage.- Complexity Classes.- Robustness of P.- Hierarchy Theorems.- Famous Problems in P.- Common Problems not Known to be in P.- The One-Million-Dollar Question.- How Hard is a Problem?.- Complete Problems.- How to Solve NP-complete Problems?.- Part III Emerging New Models of Computation - "going nano".- Molecular Computing.- Quantum Computing.- Appendix A: Further Reading - Computability and Complexity Textbooks.- Glossary.- Index.