hello and thank you for helping me understand the following:
I really don't understand this, why if language $A \in BPP$ then $A≤_P\#SAT$?
language A is in BPP class, if for a probabilistic turing machine M, M outputs 1 for all $x \in A$ in a probability $\geq 2/3$, and for all $x \not \in A$ M outputs 1 in a probability of $\leq 1/3$ and of course M must run in a polynomial time on all inputs.
so if $A \in BPP$, why does it mean that $A≤_P\#SAT$? if M is reduced to boolean F, it means that we'll get output of 1 in a probability of $\geq 2/3$ for every $x \in A$? why?
can someone please show me algorithmically or mathmatically why if language $A \in BPP$ then $A≤_P\#SAT$? quite lost
thank you, would appreciate if you could explain along.