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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 4/81 INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS A Connection to Complexity Theory Many standard computational problems on graphs are NP-complete, e.g. • Dominating Set (find a min. set of vertices neighbours to all others) • 3-Colourability (3-colour a graph without monochromatic edges) • Hamiltonian path (find a path containing every vertex exactly once) Study classes of graphs (planar graphs, graphs of bounded genus, ...) on which some of these problems become tractable. Logical approach. Instead of designing algorithms for each problem individually, formulate the problems in a logical language and design model-checking algorithms on these classes of graphs.
STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 4/81 INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS A Connection to Complexity Theory Many standard computational problems on graphs are NP-complete, e.g. • Dominating Set (find a min. set of vertices neighbours to all others) (Parametrized) definable in First-Order Logic (FO) • 3-Colourability (3-colour a graph without monochromatic edges) definable in Monadic Second-Order Logic (MSO) • Hamiltonian path (find a path containing every vertex exactly once) definable in Monadic Second-Order Logic (MSO 2 ) Study classes of graphs (planar graphs, graphs of bounded genus, ...) on which some of these problems become tractable. Logical approach. Instead of designing algorithms for each problem individually, formulate the problems in a logical language and design model-checking algorithms on these classes of graphs.
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INTRODUCTION COMPLEXITY UPPER BOUND
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