Property (ii) is particularly useful: Suppose that T is the set of random inputs that cause an algorithm to fail and the failure probability on a truly random input X is P [X ∈ T ]. If Y is an imperfect random input, then the failure probability when using Y instead of X is P [Y ∈ T ] ≤ P [X ∈ T ] + ∆(X,Y ). Property (iv) is also very powerful and we will… (More)