Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach (Encyclopedia of Mathematics and its Applications)
Cambridge University Press, 6/14/2012
EAN 9780521898331, ISBN10: 0521898331
Hardcover, 744 pages, 23.4 x 15.2 x 4.1 cm
Language: English
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.
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.