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If $\textrm{coNP}^{\textrm{NP}}=\textrm{coNP}^{L}$ for $L\in\textrm{NP}$, then does that make $L$ NP-complete?

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    $\begingroup$ No. ${}{}{}{}{}$ $\endgroup$
    – Emil Jeřábek
    Commented Oct 6 at 6:44
  • $\begingroup$ Would you please elaborate @EmilJeřábek? Is there an example of some L, known or suspected to not be NP-complete, for which this holds? $\endgroup$
    – Rincewind
    Commented Oct 6 at 18:06

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