Graph Structure and Monadic Second-Order Logic
A Language-Theoretic Approach
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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 author not only provides a thorough description of the theory, but also details 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.Read more
- 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
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- Date Published: July 2013
- format: Adobe eBook Reader
- isbn: 9781139633000
- contains: 25 b/w illus.
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
Foreword Maurice Nivat
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
Index of notation
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