The monadic second order logic of graphs VI: on several representations of graphs by relational structures

The Monadic Second-Order Logic of Graphs VII: Graphs as Relational Structures

Courcelle, B., The monadic second-order logic of graphs VII: Graphs as relational structures, Theoretical Computer Science 101 (1992) 3-33. Relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied. We define operations on structures that are compatible with monadic second-order logic, and that are powerful enough to represent c...

Circle graphs and monadic second-order logic

A circle graph is the intersection graph of a set of chords of a circle. If a circle graph is prime for the split (or join) decomposition defined by Cunnigham, it has a unique representation as a set of intersecting chords, and we prove that this representation can be defined by monadic second-order formulas. By using the (canonical) split decomposition of a circle graph, one can define in mona...

Tree-structured Graphs and Monadic Second-order Logic

Groups, Graphs, Languages, Automata, Games and Second-order Monadic Logic

In this paper we survey some surprising connections between group theory, the theory of automata and formal languages, the theory of ends, infinite games of perfect information, and monadic second-order logic.

Prefix-Recognisable Graphs and Monadic Second-Order Logic

We present several characterisations of the class of prefix-recognisable graphs including representations via graph-grammars and MSO-interpretations. The former implies that prefix-recognisable graphs have bounded clique-width; the latter is used to extend this class to arbitrary relational structures. We prove that the prefix-recognisable groups are exactly the context-free groups. Finally, we...