Complementation of rational sets on countable scattered linear orderings

@article{Rispal2004ComplementationOR,
  title={Complementation of rational sets on countable scattered linear orderings},
  author={Chloe Rispal and Olivier Carton},
  journal={Int. J. Found. Comput. Sci.},
  year={2004},
  volume={16},
  pages={767-786}
}
In a preceding paper (Bruyere and Carton, automata on linear orderings, MFCS’01), automata have been introduced for words indexed by linear orderings. These automata are a generalization of automata for finite, infinite, bi-infinite and even transfinite words studied by Buchi. Kleene’s theorem has been generalized to these words. We prove that rational sets of words on countable scattered linear ordering are closed under complementation using an algebraic approach. 

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