On the positional determinacy of edge-labeled games

@article{Colcombet2006OnTP,
  title={On the positional determinacy of edge-labeled games},
  author={Thomas Colcombet and Damian Niwinski},
  journal={Theor. Comput. Sci.},
  year={2006},
  volume={352},
  pages={190-196}
}
It is well known that games with the parity winning condition admit positional determinacy : the winner has always a positional (memoryless) strategy. This property continues to hold if edges rather than vertices are labeled. We show that in this latter case the converse is also true. That is, a winning condition over arbitrary set of colors admits positional determinacy in all games if and only if it can be reduced to a parity condition with some finite number of priorities. 

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