Search problems for two irregular coins with incomplete feedback: the underweight model

Problems of detecting two (or one of two) irregular coins x and y among a set of n coins are considered. The testing device is such that it returns feedback 1 if x belongs to the test set and y does not, while it returns feedback 0 otherwise. We present a lower bound on the worst-case number of tests necessary to nd one of the two irregular coins as well as on the worst-case number of tests to nd both of them. The lower bound improves on the information theoretic bound and shows that a \natural" algorithm to nd one coin is optimal for innnitely many values of n.