<p>We know NP<span class="math-container">$\subseteq$</span> <a href="https://en.m.wikipedia.org/wiki/Existential_theory_of_the_reals" rel="noreferrer"><span class="math-container">$\exists \mathbb R$</span></a><span class="math-container">$\subseteq$</span> PSPACE=IP, but is there some more direct proof for <span class="math-container">$\exists \mathbb R\subseteq$</span> IP?</p>

<p>What about the other direction, are there some Arthur-Merlin games that are in <span class="math-container">$\exists \mathbb R$</span>?</p>

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2019-04-24T12:08:58.433Z
Given how complicated the $\exists \mathbb{R} \subseteq \mathrm{PSPACE}$ is, a more direct proof of $\exists \mathbb{R} \subseteq \mathrm{IP}$ would be a major result. I can't find such a proof with Google.
Peter Shor 
<cc.complexity-theory><interactive-proofs><existential-theory-of-the-reals>
$\exists \mathbb R$ and IP
domotorp
# $\exists \mathbb R$ and IP

(Asked by: username_0 on 2019-04-21)

We know NP$\subseteq$ [$\exists \mathbb R$](https://en.m.wikipedia.org/wiki/Existential_theory_of_the_reals)$\subseteq$ PSPACE=IP, but is there some more direct proof for $\exists \mathbb R\subseteq$ IP?

What about the other direction, are there some Arthur-Merlin games that are in $\exists \mathbb R$?

**Tags:** cc.complexity-theory, interactive-proofs, existential-theory-of-the-reals
> **Comments:**
> **username_1**: Given how complicated the $\exists \mathbb{R} \subseteq \mathrm{PSPACE}$ is, a more direct proof of $\exists \mathbb{R} \subseteq \mathrm{IP}$ would be a major result. I can't find such a proof with Google.  

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## 0 answers

