Frequency computation and bounded queries
Richard Beigel, William I. Gasarch, Efim B. Kinber · Theoretical Computer Science · 1996
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: FaA(x1,…,xa) = A(x1)…A(xa). We are interested in the complexity (in terms of the number of queries) of approximating FaA. Let b ⩽ a and let f be any function such that FaA(x1,…,xa) and f(x1,…,xa) agree on at least b bits. For a general set A we have matching upper and lower bounds on f 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.