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.
Author(s): Neil Immerman
Series: Graduate Texts in Computer Science
Publisher: Springer
Year: 1999
Language: English
Pages: 274
Tags: Theory of Computation; Information Systems and Communication Service; Mathematical Logic and Foundations
Front Matter....Pages i-xvi
Introduction....Pages 1-3
Background in Logic....Pages 5-22
Background in Complexity....Pages 23-43
First-Order Reductions....Pages 45-55
Inductive Definitions....Pages 57-66
Parallelism....Pages 67-89
Ehrenfeucht-Fraïssé Games....Pages 91-112
Second-Order Logic and Fagin’s Theorem....Pages 113-124
Second-Order Lower Bounds....Pages 125-137
Complementation and Transitive Closure....Pages 139-155
Polynomial Space....Pages 157-168
Uniformity and Precomputation....Pages 169-180
The Role of Ordering....Pages 181-202
Lower Bounds....Pages 203-219
Applications....Pages 221-240
Conclusions and Future Directions....Pages 241-250
Back Matter....Pages 251-268
