Dewey Decimal511.3
Table Of ContentI. ALGORITHMS. 1. Problems and Algorithms. 2. Turing Machines. 3. Undecidability. 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. 6. Cryptography. 7. Approximability. 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
SynopsisThis 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 fields as computability, logic, number theory, combinatorics and probability.
LC Classification NumberQA267.7 .P36 1994