| Descriptive Complexity, Canonisation, and Definable Graph Structure Theory Contributor(s): Grohe, Martin (Author) |
|
 |
ISBN: 1107014522 ISBN-13: 9781107014527 Publisher: Cambridge University Press OUR PRICE: $194.75 Product Type: Hardcover - Other Formats Published: September 2017 |
| Additional Information |
| BISAC Categories: - Mathematics | Logic - Mathematics | Graphic Methods |
| Dewey: 511.5 |
| LCCN: 2016053731 |
| Series: Lecture Notes in Logic |
| Physical Information: 1.4" H x 6.46" W x 9.47" (1.97 lbs) 554 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting. |
Contributor Bio(s): Grohe, Martin: - Martin Grohe is a Professor of Theoretical Computer Science at RTWH Aachen University, Germany, where he holds the Chair for Logic and the Theory of Discrete Systems. His research interests are in theoretical computer science interpreted broadly, including logic, algorithms and complexity, graph theory, and database theory. |