We consider the problem of computing a function of n variables using noisy
queries, where each query is incorrect with some fixed and known probability p∈(0,1/2). Specifically, we consider the computation of the OR
function of n bits (where queries correspond to noisy readings of the bits)
and the MAX function of n real numbers (where queries correspond
to noisy pairwise comparisons). We show that an expected number of queries of
(1±o(1))DKL(p∥1−p)nlogδ1 is
both sufficient and necessary to compute both functions with a vanishing error
probability δ=o(1), where DKL(p∥1−p) denotes the
Kullback-Leibler divergence between Bern(p) and Bern(1−p)
distributions. Compared to previous work, our results tighten the dependence on
p in both the upper and lower bounds for the two functions