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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 28/81<br />
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS<br />
Courcelle’s Theorem: Algorithm<br />
Given: Graph G of tree-width ≤ k fixed MSO-formula ϕ of q.r. q<br />
1. Compute a tree-decomposition T := (T,(B t ) t∈V T) of G<br />
2. Compute the MSO q -type tp MSO (B t ) for each leaf t<br />
3. Bottom up, compute tp MSO<br />
q (G[ ⋃ t≺s B s], B t ) for each t ∈ V(T)<br />
MSO q -type of B t in G[ ⋃ t≺s B s] (graph induced by ⋃ t≺s B s)<br />
4. Check whether ϕ ∈ tp MSO<br />
q (G, B r ) at the root r of G<br />
1 2<br />
3 4<br />
5<br />
6 7 8<br />
9<br />
10 11