The Cerny conjecture for automata respecting intervals of a directed graph

@article{Grech2012TheCC,
  title={The Cerny conjecture for automata respecting intervals of a directed graph},
  author={Mariusz Grech and Andrzej Kisielewicz},
  journal={ArXiv},
  year={2012},
  volume={abs/1207.2556}
}
The Cerný's conjecture states that for every synchronizing automaton with n states there exists a reset word of length not exceeding (n-11)^2. We prove this conjecture for a class of automata preserving certain properties of intervals of a directed graph. Our result unifies and generalizes some earlier results obtained by other authors. 

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