P, NP, and NP-Completeness

The Basics of Computational Complexity

Nonfiction, Science & Nature, Mathematics, Discrete Mathematics, Computers, General Computing, Programming
Cover of the book P, NP, and NP-Completeness by Oded Goldreich, Cambridge University Press
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Author: Oded Goldreich ISBN: 9781139929776
Publisher: Cambridge University Press Publication: August 16, 2010
Imprint: Cambridge University Press Language: English
Author: Oded Goldreich
ISBN: 9781139929776
Publisher: Cambridge University Press
Publication: August 16, 2010
Imprint: Cambridge University Press
Language: English

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 not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not 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 enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.

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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 not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not 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 enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.

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