<p>Proving that <span class="math-container">$P= NP \cap$</span> co-<span class="math-container">$NP$</span> is an open problem and believed to be unlikely since Integer factoring decision problem is in both <span class="math-container">$NP$</span> and co-<span class="math-container">$NP$</span> but conjectured to be outside <span class="math-container">$P$</span>. </p>

CC BY-SA 4.0
2019-02-13T13:17:54.957Z
2019-02-13T13:17:54.957Z
Mohammad Al-Turkistany
<p>We currently don't know the relationship between NP and co-NP, but would it be possible to show whether the intersection is equal to P? I can't think of any languages in both NP and co-NP, but not in P. </p>

CC BY-SA 4.0
2019-02-13T13:13:04.193Z
Note that you can't prove that any NP problem is outside of P as that would imply that P != NP
John Dvorak
<complexity-classes><np>
Are there any known languages in the intersection of NP and co-NP but not in P?
Bert Langton
# Are there any known languages in the intersection of NP and co-NP but not in P?

(Asked by: username_0 on 2019-02-13)

We currently don't know the relationship between NP and co-NP, but would it be possible to show whether the intersection is equal to P? I can't think of any languages in both NP and co-NP, but not in P.

**Tags:** complexity-classes, np

> **Comments:**
> **username_1**: Note that you can't prove that any NP problem is outside of P as that would imply that P != NP  

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## 1 answers

### Answer by username_2 on 2019-02-13. Score: 3

Proving that $P= NP \cap$ co-$NP$ is an open problem and believed to be unlikely since Integer factoring decision problem is in both $NP$ and co-$NP$ but conjectured to be outside $P$.


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