Block Sensitivity of Weakly Symmetric Functions
Block sensitivity, which was introduced by Nisan , is one of the most useful measures of boolean functions. In this paper we investigate the block sensitivity of weakly symmetric functions (functions invariant under some transitive group action). We prove a Ω(N 1/3) lower bound for the block sensitivity of weakly symmetric functions. We also construct a weakly symmetric function which has block sensitivity Õ(N 3/7).
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