On the monadic second-order transduction hierarchy
Résumé
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.
Domaines
Logique en informatique [cs.LO]
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