lipton showed that randomized testing can be provably useful, given the problem satisfied certain properties. proving correctness of a program is one of the most important problems presented in computer science. typically in randomized testing, in order to attain a 1/1000 chance of an error, 1000 tests must be run. however lipton shows that if a problem has "easy" sub-parts, repeated black-box testing can attain "c" error rate, with "c" a constant less than 1 and "r" being the number of tests. therefore, the probability of error goes to zero exponentially fast as "r" grows.