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Article Dans Une Revue Logical Methods in Computer Science Année : 2010

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.
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Dates et versions

hal-00287223 , version 1 (11-06-2008)
hal-00287223 , version 2 (16-03-2009)
hal-00287223 , version 3 (07-04-2010)

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  • HAL Id : hal-00287223 , version 3

Citer

Achim Blumensath, Bruno Courcelle. On the monadic second-order transduction hierarchy. Logical Methods in Computer Science, 2010, 6 (2), pp.1-28. ⟨hal-00287223v3⟩

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