Descriptive Complexity, Canonisation, and Definable Graph Structure Theory (Hardcover)

Martin Grohe

ISBN 10: 1107014522 / ISBN 13: 9781107014527

Published by Cambridge University Press, Cambridge, 2017

About this Item

Hardcover. 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 The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting. This groundbreaking, yet accessible book contains original results on the interaction between graph theory and computational complexity using methods from finite model theory. As well as a wealth of new, previously unpublished results, the author also gives an account of the established results in the area. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781107014527

Bibliographic Details

• Title: Descriptive Complexity, Canonisation, and Definable Graph Structure Theory (Hardcover)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2017
• Language: English
• ISBN 10: 1107014522
• ISBN 13: 9781107014527
• Binding: Hardcover
• Condition: new

About this title

Synopsis

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.

About the Author

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.