Graph Operations, Graph Transformations and Monadic Second-Order Logic A survey

Graph structure and Monadic second-order logic

Exclusion of minor, vertex-minor, induced subgraph Tree-structuring Monadic second-order logic : expression of properties, queries, optimization functions, number of configurations. Mainly useful for tree-structured graphs (Second-order logic useless) Tools to be presented Algebraic setting for tree-structuring of graphs Recognizability = finite congruence ≡ inductive computability ≡ finite det...

The Expression of Graph Properties and Graph Transformations in Monadic Second-Order Logic

Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects

Graph structure is a flexible concept covering many different types of graph properties. Hierarchical decompositions yielding the notions of tree-width and clique-width, expressed by terms written with appropriate graph operations and associated with Monadic Second-order Logic are important tools for the construction of Fixed-Parameter Tractable algorithms and also for the extension of methods ...

Bruno Courcelle Graph Structure and Monadic Second - Order Logic

Monadic Second-Order Definable Graph Transductions: A Survey

Courcelle, B., Monadic second-order definable graph transductions: a survey, Theoretical Computer Science 126 (1994) 53-75. Formulas of monadic second-order logic can be used to specify graph transductions, i.e., multivalued functions from graphs to graphs. We obtain in this way classes of graph transductions, called monadic second-order definable graph transductions (or, more simply, d&able tr...