Block sensitivity of weakly symmetric functions

Block sensitivity, which was introduced by Nisan [Noam Nisan, CREW PRAMs and decision trees, SIAM Journal on Computing 20 (6) (1991) 999–1007. Earlier version in STOC’89], 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(N1/3) lower bound for the block sensitivity of weakly symmetric functions. We also construct a weakly symmetric function which has block sensitivity .