On the monadic second-order transduction hierarchy

Abstract

We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C ⊆ K if, and only if, there exists a transduction τ such that C ⊆ τ (K). If we only consider classes of incidence structures we can completely describe the resulting hierarchy. It is linear of order type ω+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 all trees of height n, for each n ∈ N, of all paths, of all trees, and of all grids. © A. Blumensath and B. Courcelle.