Limits of Computation

Limits of Computation: An Introduction to the Undecidable and the Intractable

Limits of Computation: An Introduction to the Undecidable and the Intractable offers a gentle introduction to the theory of computational complexity. It explains the difficulties of computation, addressing problems that have no algorithm at all and problems that cannot be solved efficiently.

The book enables readers to understand:

• What does it mean for a problem to be unsolvable or to be NP-complete?
• What is meant by a computation and what is a general model of a computer?
• What does it mean for an algorithm to exist and what kinds of problems have no algorithm?
• What problems have algorithms but the algorithm may take centuries to finish?

Developed from the authors’ course on computational complexity theory, the text is suitable for advanced undergraduate and beginning graduate students without a strong background in theoretical computer science. Each chapter presents the fundamentals, examples, complete proofs of theorems, and a wide range of exercises.

Table of Contents

Chapter 1 – Set Theory
Chapter 2 – Languages: Alphabets, Strings, and Languages
Chapter 3 – Algorithms
Chapter 4 – Turing Machines
Chapter 5 – Turing-Completeness
Chapter 6 – Undecidability
Chapter 7 – Undecidability and Reducibility
Chapter 8 – Classes NP and NP-Complete
Chapter 9 – More NP-Complete Problems
Chapter 10 – Other Interesting Questions and Classes