ON EVALUATING BOOLEAN FUNCTIONS WITH UNRELIABLE TESTS

Abstract

We consider the problem of evaluating a boolean function P(x₁,…,x_n), by asking queries of the form “x_i=?”, and receiving answers which may not always be truthful. Assuming that the total number of lies does not exceed E, we present an algorithm with cost O(n+s_PE+t_PE), where s_P is the maximal size of a minterm of P(x) and t_P ‘is the maximal size of a maxterm. We also prove that if P is monotone, then any algorithm for evaluating P must ask Ω(s_PE+t_PE) queries for some input.