Frequency of Correctness versus Average-Case Polynomial Time and   Generalized Juntas
  We prove that every distributional problem solvable in polynomial time on the average with respect to the uniform distribution has a frequently self-knowingly correct polynomial-time algorithm. We also study some features of probability weight of correctness with respect to generalizations of Procaccia and Rosenschein's junta distributions [PR07b]. 
Gabor Erdelyi, Lane A. Hemaspaandra, Joerg Rothe, Holger Spakowski