Abstract
A property of the truth table of a symmetric Boolean function is given from which one can infer a lower bound on the minimal number of 2-ary Boolean operations that are necessary to compute the function. For certain functions ofn arguments, lower bounds between roughly 2n and 5n/2 can be obtained. In particular, for eachm ≥ 3, a lower bound of 5n/2 −O(1) is established for the function ofn arguments that assumes the value 1 iff the number of arguments equal to 1 is a multiple ofm. Fixingm = 4, this lower bound is the best possible to within an additive constant.
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Stockmeyer, L.J. On the combinational complexity of certain symmetric Boolean functions. Math. Systems Theory 10, 323–336 (1976). https://doi.org/10.1007/BF01683282
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DOI: https://doi.org/10.1007/BF01683282