I would like to understand why some definitions of correctness allow a negligible failure probability. i.e. the probability that decryption reverses encryption is 1 minus a negligibly small amount.
I have noticed in the Katz, Sahai, Waters Predicate based encryption scheme that when defining correctness in the two cases where either the predicate is satisfied when trying to decrypt or when the predicate is not satisfied, there is a small failure probability only in the case when the predicate is not satisfied (I have attached an image of this).
What is the reason for the negligible probability of failure in the second case?
