E-grāmata: Computability and Complexity Theory

The theory of computing provides computer science with concepts, models, and formalisms for reasoning about the resources needed to carry out computations, and the efficiency of the computations. It provides tools to measure the difficulty of combinatorial problems both absolutely, and in comparison with other problems. This book contains material that should be core knowledge in the theory of computation for all graduate students in computer science. This comprehensive introduction begins with classical computability theory and develops complexity theory on top of that.

This volume introduces materials that are the core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations and subsequent chapters moving from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability round off the work, which focuses on the limitations of computability and the distinctions between feasible and intractable.Topics and features:*Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes*Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner; for example, about complements of complexity classes, search problems, and intermediate problems in NP*Provides key mathematical background information, including sections on logic and number theory and algebra*Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool.