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$\oplus P$ is low for itself ($\oplus P^{\oplus P}=\oplus P$).

  1. Are there other complexity classes $\mathcal D$ that satisfy $\mathcal D^{\oplus P}=\oplus P$?

  2. Are there complexity classes $\mathcal C$ that satisfy $\mathcal C^{\oplus P}=\mathcal C$?

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Weak complexity classes will satisfy $\mathcal{D}^{\oplus P} = \oplus P$. For example, $P^{\oplus P} = \oplus P$.

Strong complexity classes will satisfy $\mathcal{C}^{\oplus P} = \mathcal{C}$. For example, $\mathsf{PSPACE}^{\oplus P} = \mathsf{PSPACE}$.

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  • $\begingroup$ what is definition of weak and strong? are np and conp weak or strong? $\endgroup$ – T.... Nov 9 '17 at 19:33
  • $\begingroup$ They aren't formal terms. $\endgroup$ – Yuval Filmus Nov 9 '17 at 19:40

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