# Tagged Questions

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### Computing the permanent with polylog size matrices

The complexity of computing the permanent of a $l\times l$ binary matrix is known to be $\#\mathsf{P}$-complete, from the famous result of Valiant, where $l = \Theta(n)$. We know that the problem is ...
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### examples of use of permanents

It is known that if calculating permanent is easy, then solving hard problems in NP is easy. Is there a transparent example regarding application of say finding independent set or find chromatic ...
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### A question to the #P-complete proof of the permanent from Ben-Dor/Halevi

In the paper of Ben-Dor/Halevi [1] it is given another proof that the permanent is $\#P$-complete. In the later part of the paper, they show the reduction chain \text{IntPerm} \propto ...
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### Complexity of counting the number of Good-perfect matching in the bipartite graph

Let's $G=(U, V, E)$ be a balanced bipartite graph which $|U|=|V|=n$ and $|E|=n*(n-1)$; All nodes in $U$ are connected to all nodes in $V$ except $u_i$ to $v_i$ for $1\leq i \leq n$. Definition1: ...
In the lecture notes Introduction to Complexity Theory by Goldreich, there is a section called "How close is $\#P$ is to $NP$". It is stated there that a $P^{NP}$ machine would approximate $\#P$ in ...