We consider possible equality QMA=PP and give an argument
against it. Namely, this equality implies that PP contains PH. The argument is based on the strong form of Toda's theorem and
the strengthening of the proof for inclusion $QMA\subseteq PP$ due to Kitaev and Watrous.

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We study bounded degree graph problems, mainly the problem of
k-Dimensional Matching \emph{(k-DM)}, namely, the problem of
finding a maximal matching in a k-partite k-uniform balanced
hyper-graph. We prove that k-DM cannot be efficiently approximated
to within a factor of $ O(\frac{k}{ \ln k}) $ unless $P = NP$.
This ... more >>>

We present upper bounds on the size of codes that are locally
testable by querying only two input symbols. For linear codes, we
show that any $2$-locally testable code with minimal distance
$\delta n$ over a finite field $F$ cannot have more than
$|F|^{3/\delta}$ codewords. This result holds even ... more >>>