I try to figure out a redundant power of two-sided error randomized Karp - reduction.
It's well known fact and it is relatively hard to show that BPP is reducible by a one-sided error randomized Karp-reduction to coRP (in case of promise problem).
Without delving into details it make sense that the combination of the one - sided error probability of the reduction and the one-sided error probability of coRP leads to two-sided error probability of BPP. Of course the proof of that is not so intuitive.
The question it is possible by two-sided error randomized Karp-reduction to reduce BPP to some constant set in P? In the light of the power of one - sided randomized Karp - reduction, it make sense that two-sided randomized Karp - reduction is strong enough to reduce BPP to constant set, but how to show it formally?
Addendum:
BPP is the set of the problems that is solvable in polynomial time by two-sided error randomized algorithm, so as a result of two - sided error randomized algorithm we will get some output, them the problem in BPP can be reduced to problem P by two-sided error randomized Karp - reduction in sense that reduction is allowed to make error on both sides. Does it mean that two - sided error randomized reduction will justify the two-sided error that was made by the algorithm in solving the problem in BPP?
