Lower Bounds on Two Coin-Weighing Problems, with Applications to Threshold Circuits
نویسنده
چکیده
Among a set of n coins of two weights (good and bad), and using a balance, we wish to determine the number of bad coins using as few measurements as possible. There is a known adaptive decision tree that answers this question in O((log(n))) measurements, and a slight modification of this decision tree determines the parity of the number of bad coins in O(log n). In this paper, we prove an Ω( √ n) lower bound on the depth of any nonadaptive decision tree which solves either the counting or the parity problem. We also generalize this result to general Boolean functions, relating the coin-weighing complexity of a function to its average sensitivity. Using these results, we derive a lower bound for the size of threshold circuits for Boolean functions.
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