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/sub a//sup A/(x/sub 1/, ..., x/sub a/)=A(x/sub 1/)/spl middot//spl middot//spl middot/A(x/sub a/). We are interested in the complexity (in terms of the number of queries) of approximating F/sub a//sup A/. Let b/spl les/a and let f be any function such that F/sub a//sup A/(x/sub 1/, ..., x/sub a/) and f(x/sub 1/, ..., x/sub 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/spl ne/NP) A=SAT. We obtain exact bounds when A is the halting problem using different methods.