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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, …, x a) and f(x1, …, xa) 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



Recommended Citation

Beigel, R.; Gasarch, W.; Kinber, E., "Frequency computation and bounded queries," in Structure in Complexity Theory Conference, 1995., Proceedings of Tenth Annual IEEE , vol., no., pp.125-132, 19-22 Jun 1995 doi: 10.1109/SCT.1995.514852



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