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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 36/81<br />
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS<br />
First Step<br />
Algorithm: First Step<br />
for all v ∈ V(G)<br />
• compute N r (v)<br />
• test whether N r (v) |= ψ(v)<br />
(constant size neighbourhood)<br />
if it does, colour the vertex red<br />
Running time: O(n)<br />
O(n)<br />
O(d r ) = O(1)<br />
O(1)