On the Monadic Second-Order Transduction Hierarchy
Logic
2015-07-01 v4
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.
Cite
@article{arxiv.1004.4777,
title = {On the Monadic Second-Order Transduction Hierarchy},
author = {Achim Blumensath and Bruno Courcelle},
journal= {arXiv preprint arXiv:1004.4777},
year = {2015}
}