@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