On the monadic second-order transduction hierarchy

Achim Blumensath (1) , Bruno Courcelle (2, 3)

1 TU Darmstadt - Technische Universität Darmstadt - Technical University of Darmstadt
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 IUF - Institut universitaire de France

We compare classes of finite relational structures via monadic second-order transductions.More precisely, we study the preorder C < K : iff C is included in t(K) for some monadic second-order transduction t. If we only consider classes of incidence structures we can completely describe the resulting hierarchy. It is linear of order type omega + 3. Each level can be characterised in terms of a suitable variant of tree-width. Canonical representatives of the various levels are: the class of (i) all trees of height n, for finite n; (ii) all paths; (iii) all trees; and (iv) all grids.

Mots clés: Monadic second-order transduction; graph minor; tree

Domaines: Logique en informatique [cs.LO]

Achim Blumensath, Bruno Courcelle. On the monadic second-order transduction hierarchy. 2009. ⟨hal-00287223v2⟩