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

Bruno Courcelle and Joost Engelfriet Graph Structure and Monadic Second - Order Logic , a Language Theoretic Approach

Bruno Courcelle and Joost Engelfriet Graph Structure and Monadic Second - Order Logic , a Language Theoretic Approach April 2011 to be published by Cambridge University

Bruno Courcelle Graph Structure and Monadic Second - Order Logic , a Language Theoretic

Graph equivalences and decompositions definable in Monadic Second-Order Logic. The case of Circle Graphs

Many graph properties and graph transformations can be formalized inMonadic Second-Order logic. This language is the extension of First-Order logic allowing variables denoting sets of elements. In the case of graphs, these elements can be vertices, and in some cases edges. Monadic second-order graph properties can be checked in linear time on the class of graphs of tree-width at most k for any ...

Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications

This tutorial will present an overview of the use of Monadic Second-Order Logic to describe sets of finite graphs and graph transformations, in relation with the notions of tree-width and clique-width. It will review applications to the construction of algorithms, to Graph Theory and to the extension to graphs of Formal Language Theory concepts. We first explain the role of Logic. A graph, eith...

The Monadic Second-Order Logic of Graphs. I. Recognizable Sets of Finite Graphs

This paper begins an investigation of the monadic second-order logic of graphs and of sets of graphs, using techniques from universal algebra, and the theory of formal languages. (By a graph, we mean a finite directed hyperedge-labelled hypergraph, equipped with a sequence of distinguished vertices.) A survey of this research can be found in Courcelle [ 111. An algebraic structure on the set of...