On the State Complexity of the Reverse of - and -Trivial Regular Languages

@inproceedings{Jirskov2013OnTS,
  title={On the State Complexity of the Reverse of - and -Trivial Regular Languages},
  author={Galina Jir{\'a}skov{\'a} and Tomas Masopust},
  booktitle={DCFS},
  year={2013}
}
The tight bound on the state complexity of the reverse of \({\mathcal R}\)-trivial and \({\mathcal J}\)-trivial regular languages of the state complexity n is 2 n − 1. The witness is ternary for \({\mathcal R}\)-trivial regular languages and (n − 1)-ary for \({\mathcal J}\)-trivial regular languages. In this paper, we prove that the bound can be met neither by a binary \({\mathcal R}\)-trivial regular language nor by a \({\mathcal J}\)-trivial regular language over an (n − 2)-element alphabet… 
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