State complexity of combined operations with two basic operations

@article{Cui2012StateCO,
  title={State complexity of combined operations with two basic operations},
  author={Bo Cui and Yuan Gao and Lila Kari and Sheng Yu},
  journal={Theor. Comput. Sci.},
  year={2012},
  volume={437},
  pages={82-102}
}
This paper studies the state complexity of (L1L2) , L1 L2, L ∗ 1L2, (L1 ∪L2)L3, (L1∩L2)L3, L1L2∩L3, and L1L2∪L3 for regular languages L1, L2, and L3. We first show that the upper bound proposed by [Liu, Martin-Vide, Salomaa, Yu, 2008] for the state complexity of (L1L2) R coincides with the lower bound and is thus the state complexity of this combined operation by providing some witness DFAs. Also, we show that, unlike most other cases, due to the structural properties of the result of the first… CONTINUE READING

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