Elements of The Theory of Computation

The aim of this textbook is to present an account of the theory of computation. After introducing the concept of a model of computation and presenting various examples, the author explores the limitations of effective computation via basic recursion theory. Self-reference and other methods are introduced as fundamental and basic tools for constructing and manipulating algorithms.

The theory of computation is used to address challenges arising in many computer science areas such as artificial intelligence, language processors, compiler writing, information and coding systems, programming language design, computer architecture and more. To grasp topics concerning this theory readers need to familiarize themselves with its computational and language models, based on concepts of discrete mathematics including sets, relations, functions, graphs and logic.

Introduction to Languages and the Theory of Computation helps students make the connection between the practice of computing and an understanding of the profound ideas that defines it. The book's organization and the author's ability to explain complex topics clearly make this introduction to the theory of computation an excellent resource for a broad range of upper level students.

This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable.