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I tried to prove or disprove that pp is closed under cook reductions. anyone has a idea or link to a answer?

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PH $\subseteq$ PPP ​ is known to hold, so if PP is closed under Cook reductions
then ​ PH $\subseteq$ PPP $\subseteq$ PPPP $\subseteq$ PP . ​ ​ ​ ​ ( PH $\subseteq$ PP ​ is not known to hold.)

If ​ PP = PSPACE ​ then ​ PPPP = PPPSPACE = PSPACE = PP .
( PP ≠ PSPACE ​ is not known to hold.)

See the Counting Hierarchy.

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  • $\begingroup$ i don't sure if i understand your question. you said it's a open question? $\endgroup$ – evyatar Jun 21 '16 at 14:19
  • $\begingroup$ I didn't ask a question here. ​ ​ $\endgroup$ – user12859 Jun 21 '16 at 22:37
  • $\begingroup$ i meam your answer $\endgroup$ – evyatar Jun 22 '16 at 12:20

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