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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 72/81 INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS Another Good Idea, A Little Less Wrong We reduce the propositional satisfiability problem (SAT) to MC(MSO,C). Given: w := (X 1 ∨ X 2 ∨¬X 3 )∧(X 4 ∨¬X 5 ∨ X 6 )... Problem: Decide if w is satisfiable. Reduction. Compute G w |w| 28 < tw(G w ) Comp. GM (P,Q) MSO-definable. There is MSO 2 -formula ϕ(P, Q) saying (P, Q) are grid-like minor.
STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 72/81 INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS Another Good Idea, A Little Less Wrong We reduce the propositional satisfiability problem (SAT) to MC(MSO,C). Given: w := (X 1 ∨ X 2 ∨¬X 3 )∧(X 4 ∨¬X 5 ∨ X 6 )... Problem: Decide if w is satisfiable. Reduction. Compute G w |w| 28 < tw(G w ) I(P,Q) Comp. GM (P,Q) MSO-definable. There is MSO 2 -formula ϕ(P, Q) saying (P, Q) are grid-like minor.
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Towards a Structural Characterisati
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STEPHAN KREUTZER COMPLEXITY OF MODE
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