Synopses & Reviews
This new text offers a comprehensive and accessible treatment of the theory of algorithms and complexity - the elegant body of concepts and methods developed by computer scientists over the past 30 years for studying the performance and limitations of computer algorithms. Among topics covered are: reductions and NP-completeness, cryptography and protocols, randomized algorithms, and approximability of optimization problems, circuit complexity, the "structural" aspects of the P=NP question, parallel computation, the polynomial hierarchy, and many others.
Several sophisticated and recent results are presented in a rather simple way, while many more are developed in the form of extensive notes, problems, and hints. The book is surprisingly self-contained, in that it develops all necessary mathematical prerequisites from such diverse field as computability, logic, number theory, combinatorics, and probability. Features
- First unified introduction to computational complexity.
- Integrates computation, applications, and logic throughout.
- Provides an accessible introduction to logic, including Boolean logic, first-order logic, and second-order logic.
- Includes extensive exercises including historical notes, references, and challeging problems.
This introduction to computational complexity integrates computation, applications and logic. The book considers logic, including boolean logic, first-order logic and second-order logic. It also includes extensive exercises and challenging problems.
The first unified introduction and reference for the field of computational complexity. Virtually non-existent only 25 years ago, computational complexity has expanded tremendously and now comprises a major part of the researh activity in theoretical science.
Table of Contents
I. ALGORITHMS. 1. Problems and Algorithms.
2. Turing Machines.
II. LOGIC. 1. Boolean Logic.
2. First Order Logic.
3. Undecidability in Logic.
III. P AND NP. 1. Relations between Complexity Classes.
2. Reductions and Completeness.
3. NP-Complete Problems.
4. coNP and Function Problems.
5. Randomized Computation.
8. On P vs. NP.
IV. INSIDE P. 1. Parallel Computation.
2. Logarithmic Space.
V. BEYOND NP. 1. The Polynomial Hierarchy.
2. Computation That Counts.
3. Polynomial Space.
4. A Glimpse Beyond. 0201530821T04062001