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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 35/81<br />
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS<br />
Proof of Theorem<br />
Suppose<br />
∧<br />
m∧<br />
ϕ := ∃x 1 ...∃x m dist(x i , x j ) > 2r ∧ ψ(x i )<br />
for some r-local formula ψ(x).<br />
Let G be a graph of maximum degree d.<br />
1≤i 2r whose r-neighbourhoods satisfy ψ.
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