Reactive Systems Group

Down the Borel Hierarchy: Solving Muller Games via Safety Games

Daniel Neider, Rabinovich and Martin Zimmermann

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@inproceedings{NRZ12a,
  author =      {Neider, Daniel and Rabinovich, Roman and  Zimmermann, Martin},
  title =       {Down the {B}orel {H}ierarchy: {S}olving {M}uller {G}ames via {S}afety {G}ames},
  booktitle =   {Proceedings of the Third International Symposium on Games, Automata, Logic, and Formal Verification, GandALF 2012},
  year =        {2012},
  editor =      {Faella, M. and Murano, A.},
  series =   {Electronic {P}roceedings in {T}heoretical {C}omputer {S}cience},
  volume =      {96},
  pages =       {169--182},
  abstract =    {We transform a Muller game with n vertices into a safety game with (n!)^3
vertices whose solution allows to determine the winning regions of the Muller
game and to compute a finite-state winning strategy for one player. This yields
a novel antichain-based memory structure and a natural notion of permissive
strategies for Muller games. Moreover, we generalize our construction by
presenting a new type of game reduction from infinite games to safety games and
show its applicability to several other winning conditions.}
}

We transform a Muller game with n vertices into a safety game with (n!)^3 vertices whose solution allows to determine the winning regions of the Muller game and to compute a finite-state winning strategy for one player. This yields a novel antichain-based memory structure and a natural notion of permissive strategies for Muller games. Moreover, we generalize our construction by presenting a new type of game reduction from infinite games to safety games and show its applicability to several other winning conditions.

Third International Symposium on Games, Automata, Logic, and Formal Verification