Foundations and TrendsŪ in Theoretical Computer Science
A SURVEY OF LOWER BOUNDS FOR SATISFIABILITY AND RELATED PROBLEMS
by Dieter van Melkebeek (University of Wisconsin, USA)
NP-completeness arguably forms the most pervasive concept from computer science as it captures the computational complexity of thousands of important problems from all branches of science and engineering. The P versus NP question asks whether these problems can be solved in polynomial time. A negative answer has been widely conjectured for a long time but, until recently, no concrete lower bounds were known on general models of computation.
Satisfiability is the problem of deciding whether a given Boolean formula has at least one satisfying assignment. It is the first problem that was shown to be NP-complete, and is possibly the most commonly studied NP-complete problem, both for its theoretical properties and its applications in practice.
A Survey of Lower Bounds for Satisfiability and Related Problems surveys the recently discovered lower bounds for the time and space complexity of satisfiability and closely related problems. It overviews the state-of-the-art results on general deterministic, randomized, and quantum models of computation, and presents the underlying arguments in a unified framework.
A Survey of Lower Bounds for Satisfiability and Related Problems is an invaluable reference for professors and students doing research in complexity theory, or planning to do so.
Published by Now Publishers and marketed by World Scientific
Contents:
- Introduction
- Preliminaries
- Common Structure of the Arguments
-
Deterministic Algorithms
- Nondeterministic Algorithms
- Somewhat-Nonuniform Algorithms
- Randomized Algorithms
- Quantum Algorithms
- Future Directions
- Acknowledgements
- References
Readership: Postgraduates, researchers and professors, especially computer
scientists (algorithm designers, complexity theorists), physicists, mathematicians and other scientists.
| 116pp |
Pub. date: Oct 2007 |
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