On the model-checking of monadic second-order formulas with edge set quantifications.

Bruno Courcelle (1, 2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 IUF - Institut universitaire de France

In order to obtain fixed-parameter tractable model-checking algorithms for monadic second-order graph properties that depend on the multiplicities of edges, we extend clique-width to graphs with multiple edges, and we extend counting monadic second-order logic accordingly. For monadic second-order graph properties that need edge set quantifications in their logical expressions, we define a graph complexity measure called special tree-width. Its value is between path-width and tree-width. We study its main properties and we explain why it is better that tree-width.

Mots clés: tree-width; clique-width; monadic second-order logic

Domaines: Logique en informatique [cs.LO]

Bruno Courcelle. On the model-checking of monadic second-order formulas with edge set quantifications.. Discrete Applied Mathematics, 2012, 160, pp.866-887. ⟨10.1016/j.dam.2010.12.017⟩. ⟨hal-00481735v2⟩