How Deterministic are Good-For-Games Automata?

@article{Boker2017HowDA,
  title={How Deterministic are Good-For-Games Automata?},
  author={Udi Boker and Orna Kupferman and Michal Skrzypczak},
  journal={ArXiv},
  year={2017},
  volume={abs/1710.04115}
}
In GFG automata, it is possible to resolve nondeterminism in a way that only depends on the past and still accepts all the words in the language. The motivation for GFG automata comes from their adequacy for games and synthesis, wherein general nondeterminism is inappropriate. We continue the ongoing effort of studying the power of nondeterminism in GFG automata. Initial indications have hinted that every GFG automaton embodies a deterministic one. Today we know that this is not the case, and… 

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