Blumensath, Achim and Courcelle, Bruno - On the Monadic Second-Order Transduction Hierarchy

lmcs:1208 - Logical Methods in Computer Science, June 22, 2010, Volume 6, Issue 2
On the Monadic Second-Order Transduction Hierarchy

Authors: Blumensath, Achim and Courcelle, Bruno

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.


Source : oai:arXiv.org:1004.4777
DOI : 10.2168/LMCS-6(2:2)2010
Volume: Volume 6, Issue 2
Published on: June 22, 2010
Submitted on: June 25, 2008
Keywords: Mathematics - Logic,G.2.2,F.4.1


Share

Consultation statistics

This page has been seen 49 times.
This article's PDF has been downloaded 9 times.