<blockquote>
  <p><strong>Possible Duplicate:</strong><br>
  <a href="https://cstheory.stackexchange.com/questions/529/does-vp-neq-vnp-imply-p-neq-np">Does $VP \neq VNP$ imply $P \neq NP$?</a>  </p>
</blockquote>



<p>In his GCT papers Mulmuley first starts with the #P/NC question. And then gets into setting up a roadmap for how to show obstructions ( some sort of Weyl modules I gathered, if they can be constructed) could potentially rule out embedding of a class variety into another. </p>

<p>Is it clear, and almost obvious how that chain of argument ( if and when fleshed out) will automatically extend for P/NP separation? I am not a TCS expert - so I wonder if I am missing something obvious.</p>

CC BY-SA 3.0
2011-07-10T20:52:20.193Z
See this question: http://cstheory.stackexchange.com/questions/529/does-vp-neq-vnp-imply-p-neq-np
Aaron Sterling
CC BY-SA 3.0
2011-08-07T03:23:48.223Z
FYI, @Arnab asked about how the GCT chain of argument extends to $P$ vs $NP$, and there is actually a reasonable answer, beyond the answers to the question of whether $VP \neq VNP$ implies $P \neq NP$. In brief, one can associate certain functions to $P$ and $NP$ and use those functions in place of $det$ and $perm$, and then the whole GCT chain of reasoning goes through for those functions. There are a few important technical issues to be discussed about this, but that is the idea, and the technical issues do not fit in a comment.
Joshua Grochow
<gct>
From Determinant-Permanent to P-NP
Arnab
# From Determinant-Permanent to P-NP

(Asked by: username_0 on 2011-07-10)

> **Possible Duplicate:**  
> [Does $VP \neq VNP$ imply $P \neq NP$?](https://cstheory.stackexchange.com/questions/529/does-vp-neq-vnp-imply-p-neq-np)

In his GCT papers Mulmuley first starts with the #P/NC question. And then gets into setting up a roadmap for how to show obstructions ( some sort of Weyl modules I gathered, if they can be constructed) could potentially rule out embedding of a class variety into another.

Is it clear, and almost obvious how that chain of argument ( if and when fleshed out) will automatically extend for P/NP separation? I am not a TCS expert - so I wonder if I am missing something obvious.

**Tags:** gct
> **Comments:**
> **username_1**: See this question: http://cstheory.stackexchange.com/questions/529/does-vp-neq-vnp-imply-p-neq-np  
> **username_2**: FYI, @Arnab asked about how the GCT chain of argument extends to $P$ vs $NP$, and there is actually a reasonable answer, beyond the answers to the question of whether $VP \neq VNP$ implies $P \neq NP$. In brief, one can associate certain functions to $P$ and $NP$ and use those functions in place of $det$ and $perm$, and then the whole GCT chain of reasoning goes through for those functions. There are a few important technical issues to be discussed about this, but that is the idea, and the technical issues do not fit in a comment.  

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