Evaluation of DNF Formulas

We consider the Stochastic Boolean Function Evaluation (SBFE) problem for classes of DNF formulas. The SBFE problem for DNF formulas is a “sequential testing” problem where we need to determine the value of DNF formula on an initially unknown input x = (x1, ..., xn), when there is a cost ci associated with obtaining the value of xi, each xi is equal to 1 with known probability pi, and the xi are independent. The goal is to minimize expected cost. The SBFE problem is inapproximable for general DNF formulas. We give approximate and exact algorithms for two subclasses of DNF formulas: monotone k-DNF and monotone k-term DNF. We also prove a lower bound result for evaluation of monotone CDNF formulas.