Graph Structure and Monadic Second-Order Logic
Graph Structure and Monadic Second-Order Logic
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
- Synthesizes the authors' substantial body of research over the last 20 years
- Contains useful tools for readers interested in graph theory
- Book's coverage and style makes it the definitive reference for graduate students and researchers
Reviews & endorsements
'In its huge breadth and depth the authors manage to provide a comprehensive study of monadic second-order logic on graphs covering almost all aspects of the theory that can be presented from a language theoretical or algebraic point of view. There is currently no other textbook or any other source that matches the range of materials covered in this book. As such it is a fantastic resource for those who to study this area [and] will undoubtedly turn into the standard reference for this area.' Stephan Kreutzer, Mathematical Reviews
Product details
No date availableHardback
9780521898331
744 pages
240 × 160 × 41 mm
1.27kg
25 b/w illus.
Table of Contents
- Foreword Maurice Nivat
- Introduction
- 1. Overview
- 2. Graph algebras and widths of graphs
- 3. Equational and recognizable sets in many-sorted algebras
- 4. Equational and recognizable sets of graphs
- 5. Monadic second-order logic
- 6. Algorithmic applications
- 7. Monadic second-order transductions
- 8. Transductions of terms and words
- 9. Relational structures
- Conclusion and open problems
- References
- Index of notation
- Index.
