Slides.

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