State complexity of deletion and bipolar deletion

@article{Han2015StateCO,
  title={State complexity of deletion and bipolar deletion},
  author={Yo-Sub Han and Sang-Ki Ko and Kai Salomaa},
  journal={Acta Informatica},
  year={2015},
  volume={53},
  pages={67-85}
}
It is well known that the language obtained by deleting an arbitrary language from a regular language is regular. We give an upper bound for the state complexity of deleting an arbitrary language from a regular language and a matching lower bound. We show that the state complexity of deletion is $$n \cdot 2^{n-1}$$ n · 2 n - 1 [respectively, $$(n + \frac{1}{2}) \cdot 2^n - 2$$ ( n + 1 2 ) · 2 n - 2 ] when using complete (respectively, incomplete) deterministic finite automata. We show that the… CONTINUE READING
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