Descriptive Complexity
By: by Neil Immerman
Series: Graduate Texts in Computer Science; Graduate texts in computer science
Publisher: Springer New York
Published: 1999
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 268
ISBN-13: 9781461268093; 9781461205395
Subjects: Information systems; Symbolic and mathematical Logic; Computer science; Information theory
Description: A basic issue in computer science is the complexity of problems. Computational complexity measures how much time or memory is needed as a function of the input problem size. Descriptive complexity is concerned with problems which may be described in first-order logic. By virtue of the close relationship between logic and relational databses, it turns out that this subject has important applications to databases such as analysing the queries computable in polynomial time, analysing the parallel time needed to compute a query, and the analysis of nondeterministic classes. This book is written as a graduate text and so aims to provide a reasonably self-contained introduction to this subject. The author has provided numerous examples and exercises to further illustrate the ideas presented.
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Table of contents: title: Introduction; title: Background in Logic; title: Background in Complexity; title: First-Order Reductions; title: Inductive Definitions; title: Parallelism; title: Ehrenfeucht-Fraisse Games; title: Second-Order Logic and Fagin's Theorem; title: Second-Order Lower Bounds; title: Complementation and Transitive Closure; title: Polynomial Space; title: Uniformity and Precomputation; title: The Role of Ordering; title: Lower Bounds; title: Applications; title: Conclusions and Future Directions.