The Boolean Hierarchy over Level 1/2 of the Straubing-Therien Hierarchy

@article{Schmitz1998TheBH,
  title={The Boolean Hierarchy over Level 1/2 of the Straubing-Therien Hierarchy},
  author={Heinz Schmitz and Klaus W. Wagner},
  journal={CoRR},
  year={1998},
  volume={cs.CC/9809118}
}
For some fixed alphabet A with |A| ≥ 2, a languageL ⊆ A is in the classL1/2 of the Straubing-Thérien hierarchy if and only if it can be expres sed as a finite union of languages A∗a1A ∗a2A ∗ · · ·A∗anA∗, whereai ∈ A andn ≥ 0. The classL1 is defined as the boolean closure ofL1/2. It is known that the classes L1/2 andL1 are decidable. We give a membership criterion for the single classes of the boolean hierarchy ov erL1/2. From this criterion we can conclude that this boolean hierarchy is proper… CONTINUE READING

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