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 \subseteq K if, and only if, there exists a transduction {\tau} such that C\subseteq{\tau}(K). 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 all trees of height n, for each n \in N, of all paths, of all trees, and of all grids.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2010
- DOI:
- 10.48550/arXiv.1004.4777
- arXiv:
- arXiv:1004.4777
- Bibcode:
- 2010arXiv1004.4777B
- Keywords:
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- Mathematics - Logic;
- G.2.2;
- F.4.1
- E-Print:
- Logical Methods in Computer Science, Volume 6, Issue 2 (June 22, 2010) lmcs:1208