I am thinking of the equality "PCP(O(log(n)),0) = P"
Say I have a deterministic polynomial time algorithm $A$ whose correctness I can't prove immediately. But say I create a probabilistic version of this algorithm say $A_P$ such that it uses log(n) random bits. Now if I prove somekind of (exactly what ?) expectation correctness of $A_P$ then does it imply that $A$ was correct?
If the above is not right then I would like if someone can point me to what is the closest correct thing to this!