van den Heuvel, Jan, Kreutzer, Stephan, Pilipczuk, Michal, Quiroz, Daniel, Rabinovich, Roman and Siebertz, Sebastian
(2017)
Modelchecking for successorinvariant firstorder formulas on graph classes of bounded expansion.
In: 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, 20170620  20170623.
(In Press)
Abstract
A successorinvariant firstorder formula is a formula that has access to an auxiliary successor relation on a structure's universe, but the model relation is independent of the particular interpretation of this relation. It is well known that successorinvariant formulas are more expressive on finite structures than plain firstorder formulas without a successor relation. This naturally raises the question whether this increase in expressive power comes at an extra cost to solve the modelchecking problem, that is, the problem to decide whether a given structure together with some (and hence every) successor relation is a model of a given formula. It was shown earlier that adding successorinvariance to firstorder logic essentially comes at no extra cost for the modelchecking problem on classes of finite structures whose underlying Gaifman graph is planar [1], excludes a fixed minor [2] or a fixed topological minor [3], [4]. In this work we show that the modelchecking problem for successorinvariant formulas is fixedparameter tractable on any class of finite structures whose underlying Gaifman graphs form a class of bounded expansion. Our result generalises all earlier results and comes close to the best tractability results on nowhere dense classes of graphs currently known for plain firstorder logic.
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