Differential Games, Locality, and Model Checking for FO Logic of Graphs

Authors Jakub Gajarský, Maximilian Gorsky, Stephan Kreutzer

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Author Details

Jakub Gajarský
  • University of Warsaw, Poland
Maximilian Gorsky
  • TU Berlin, Germany
Stephan Kreutzer
  • TU Berlin, Germany

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Jakub Gajarský, Maximilian Gorsky, and Stephan Kreutzer. Differential Games, Locality, and Model Checking for FO Logic of Graphs. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We introduce differential games for FO logic of graphs, a variant of Ehrenfeucht-Fraïssé games in which the game is played on only one graph and the moves of both players are restricted. We prove that these games are strong enough to capture essential information about graphs from graph classes which are interpretable in nowhere dense graph classes. This, together with the newly introduced notion of differential locality and the fact that the restriction of possible moves by the players makes it easy to decide the winner of the game in some cases, leads to a new approach to the FO model checking problem which can be used on various graph classes interpretable in classes of sparse graphs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
  • Theory of computation → Fixed parameter tractability
  • FO model checking
  • locality
  • Gaifman’s theorem
  • EF games


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