We know that for every counting problem $\#A$ in $\#P$, there is a probabilistic algorithm $\mathcal C$ that on input $x$, computes with high probability a value $v$ such that $$(1 − ε)\#A(x) ≤ v ≤ (1 + ε)\#A(x)$$ in time polynomial in $|x|$ and within $\frac1ε$ multiplicative factor, using an oracle for $NP$.

That is $\#P$ can be approximated in $BPP^{NP}$.

What is the best derandomization result for this that is known?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.