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Backtracking Games and Inflationary Fixed Points

  • Anuj Dawar
  • Erich Grädel
  • Stephan Kreutzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)

Abstract

We define a new class of games, called backtracking games. Backtracking games are essentially parity games with an additional rule allowing players, under certain conditions, to return to an earlier position in the play and revise a choice.

This new feature makes backtracking games more powerful than parity games. As a consequence, winning strategies become more complex objects and computationally harder. The corresponding increase in expressiveness allows us to use backtracking games as model checking games for inflationary fixed-point logics such as IFP or MIC. We identify a natural subclass of backtracking games, the simple games, and show that these are the “right” model checking games for IFP by a) giving a translation of formulae φ and structures \(\cal A\) into simple games such that \(\cal A \models \phi\) if, and only if, Player 0 wins the corresponding game and b) showing that the winner of simple backtracking games can again be defined in IFP.

Keywords

Model Check Simple Game Winning Strategy Point Logic Game Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Anuj Dawar
    • 1
  • Erich Grädel
    • 2
  • Stephan Kreutzer
    • 3
  1. 1.University of Cambridge Computer LaboratoryCambridgeUK
  2. 2.Mathematische Grundlagen der InformatikAachen-University 
  3. 3.Logik in der InformatikHumboldt-UniversityBerlin

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