Slides.

STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 57/81
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS
General Proof Idea
We reduce the propositional satisfiability problem (SAT) to MC(MSO,C).
Given: (X 1 ∨ X 2 ∨¬X 3 )∧(X 4 ∨¬X 5 ∨ X 6 )... ˆ= w ∈ {0, 1} ∗
Problem: Decide if w is satisfiable.
Reduction.
1. Construct G w ∈ C of tree-width |w| c with tw(G w ) > log d |G w |
2. Somehow encode w in a sub-graph of G w
Use obstructions to tree-width.
Condition 1: G w exists in C
Condition 2: G w can be computed efficiently
use closure under sub-graphs
3. Define an MSO-formula ϕ (independent of w) which is true in G w iff
w is satisfiable.
ϕ decodes w in G w and decides whether w is satisfiable.