Slides.

More documents

Recommendations

Info

STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 41/81 INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS Local Model Checking Essentially: • We need to be able to test r-local formulae ψ(x) in r ′ -neighbourhoods Here: r, r ′ depend on the original formula ϕ and hence are constant (part of the parameter).
STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 42/81 INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS Local Model Checking Theorem: Let C be a class of graphs such that the following is fpt: LOCAL-FO-MC(C) Input: ϕ ∈ FO, Graph G ∈ C,v 1 ,...,v k ∈ V(G), and r ∈ N Parameter: r + k +|ϕ| Problem: Decide G [ Nr G (v 1 ,...,v k )] |= ϕ Then first-order model checking is fixed-parameter tractable on C. Consequences: For efficient first-order model checking, it suffices if every neighbourhood in a graph is “well-behaved”. Not the whole graph needs to have small tree-width, but only its neighbourhoods.
Page 1 and 2:
Towards a Structural Characterisati
Page 3 and 4:
STEPHAN KREUTZER COMPLEXITY OF MODE
Page 5 and 6:
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32: STEPHAN KREUTZER COMPLEXITY OF MODE
Page 81: STEPHAN KREUTZER COMPLEXITY OF MODE
Page 91 and 92: INTRODUCTION COMPLEXITY UPPER BOUND
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
show all

Slides.

Create successful ePaper yourself

Delete template?

Save as template?