On the Monadic Second-Order Transduction Hierarchy

@article{Blumensath2010OnTM,
  title={On the Monadic Second-Order Transduction Hierarchy},
  author={Achim Blumensath and Bruno Courcelle},
  journal={Logical Methods in Computer Science},
  year={2010},
  volume={6}
}
We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder C ⊑ K : iff C ⊆ τ(K) for some transduction τ . 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… CONTINUE READING

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