# $P=PP$ or $P=PSPACE$ vs $VP=VNP$

We do not know if $$P=NP$$ has an impact on $$VP=VNP$$ however how about $$P=PP$$?

1. Is $$PP$$ and $$VNP$$ related and would $$P=PP$$ or $$P=PSPACE$$ imply $$VP=VNP$$?

2. Is there a way to show $$\#P$$ is in $$FP^{PP}$$?

Note that $$\#P\in FP^{PP}$$ follows from a simple binary search. Given some non-deterministic machine $$M$$, the language $$\{(x,k) |\#M(x)\ge k\}$$, where $$\#M(x)$$ is the number of accepting paths on input $$x$$, is in PP (you can change the constant in the definition of PP to any FP function). Thus, using a PP oracle we can count the number of accepting paths via binary search.
This implies that $$\mathsf{P=PP}$$ puts permanent in $$VP$$, as the problem of counting the number of perfect matchings in a bipartite graph (or equivalently, computing the permanent of the adjacency matrix) is in $$\#P$$.