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- Bruno Courcelle
- Inf. Comput.
- 1990

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 [… (More)

- Bruno Courcelle
- Handbook of Theoretical Computer Science, Volume…
- 1990

- Bruno Courcelle, Johann A. Makowsky, Udi Rotics
- Theory of Computing Systems
- 1998

Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs of tree-width at most k , i.e., that have tree decompositions of width at most k , where k is fixed, every decision or optimization problem expressible in monadic… (More)

- Bruno Courcelle, Stephan Olariu
- Discrete Applied Mathematics
- 2000

A graph complexity measure that we call clique-width is associated in a natural way with certain graph decompositions, more or less like tree-width is associated with tree-decomposition which are, actually, hierarchical decompositions of graphs. In general, a decomposition of a graph G can be viewed as a nite term, written with appropriate operations on… (More)

- Bruno Courcelle
- Theor. Comput. Sci.
- 1996

Graphs are finite and handled as relational structures. We give some answers to the following general questions: (1) For which classes of graphs % is it possible to specify a linear ordering of the set of vertices of each graph of ‘8 by fixed monadic second-order formulas? (2) For which classes of graphs V does there exist an extension 2 of monadic… (More)

- Bruno Courcelle
- Theor. Comput. Sci.
- 1983

- Bruno Courcelle
- Handbook of Graph Grammars
- 1997

- Michel Bauderon, Bruno Courcelle
- Mathematical systems theory
- 1987

We define an algebraic structure for the set of finite graphs, a notion of graph expression for defining them, and a complete set of equational rules for manipulating graph expressions. (By agraph we mean an oriented hypergraph, the hyperedges of which are labeled with symbols from a fixed finite ranked alphabet and that is equipped with a finite sequence… (More)

- Bruno Courcelle
- Mathematical systems theory
- 1989

A countable graph can be considered as the value of a certain infinite expression, represented itself by an infinite tree. We establish that the set of finite or infinite (expression) trees constructed with a finite number of operators, the value of which is a graph satisfying a property expressed in monadic second-order logic, is itself definable in… (More)

- Bruno Courcelle
- ITA
- 1992