2010 | OriginalPaper | Chapter
The Complexity of Satisfaction on Sparse Graphs
Author : Anuj Dawar
Published in: Parameterized and Exact Computation
Publisher: Springer Berlin Heidelberg
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We consider the complexity of deciding, given a graph
G
and a formula
φ
of first-order logic in the language of graphs, whether or not
G
⊧
φ
. In other words, we are interested in the complexity of the satisfaction relation for first-order logic on graphs. More particularly, we look at the complexity of this problem parameterized by the length of the formula
φ
. This problem (which is known to be
AW
[*]-complete) includes as special cases many important graph-theoretic problems, including
Independent Set, Dominating Set
and complete problems at all levels of the
W
-hierarchy.