The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or t finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or t discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly eugh, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.
Oded Goldreich is a Professor of Computer Science at the Weizmann Institute of Science and an incumbent of the Meyer W. Weisgal Professorial Chair. He is an editor for the SIAM Journal on Computing, the Journal of Cryptology, and Computational Complexity and previously authored the books Modern Cryptography, Probabilistic Proofs and Pseudorandomness, the two-volume work Foundations of Cryptography, and Computational Complexity: A Conceptual Perspective.