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Graph Structure and Monadic Second-Order Logic
A Language-Theoretic Approach

$185.00 (C)

Part of Encyclopedia of Mathematics and its Applications

Maurice Nivat
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  • Date Published: July 2012
  • availability: Available
  • format: Hardback
  • isbn: 9780521898331

$ 185.00 (C)
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About the Authors
  • 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.

    • 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
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    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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    Product details

    • Date Published: July 2012
    • format: Hardback
    • isbn: 9780521898331
    • length: 744 pages
    • dimensions: 234 x 152 x 41 mm
    • weight: 1.27kg
    • contains: 25 b/w illus.
    • availability: Available
  • 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.

  • Resources for

    Graph Structure and Monadic Second-Order Logic

    Bruno Courcelle, Joost Engelfriet

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  • Authors

    Bruno Courcelle, Université de Bordeaux
    Bruno Courcelle is a Professor at Bordeaux 1 University and a member of LaBRI (the Bordeaux Laboratory of Computer Science, CNRS) and of the Institut Universitaire de France. After studying at the École Normale Supérieure, he was a researcher at INRIA (1972–8), before becoming a Professor at Bordeaux in 1979. He obtained his PhD (supervised by M. Nivat), in 1976. He is on the editorial boards for the journals Information and Computation and Logical Methods in Computer Science.

    Joost Engelfriet, Universiteit Leiden

    Contributors

    Maurice Nivat

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