Frequency computation and bounded queries

There have been several papers over the last ten years that consider the number of queries needed to compute a function as a measure of its complexity. The following function has been studied extensively in that light: F_a^A(x₁, …, x_a)=A(x₁)···A(x_a). We are interested in the complexity (in terms of the number of queries) of approximating F_a^A. Let b⩽a and let f be any function such that F_a^A(x₁, …, x _a) and f(x₁, …, x_a) agree on at least b bits. For a general set A we have matching upper and lower bounds that depend on coding theory. These are applied to get exact bounds for the case where A is semirecursive, A is superterse, and (assuming P≠NP) A=SAT. We obtain exact bounds when A is the halting problem using different methods