Block sensitivity of weakly symmetric functions

Authors:
Xiaoming Sun
Affiliations:
Center for Advanced Study, Tsinghua University
Venue:
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Year:
2006

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Abstract

Block sensitivity, which was introduced by Nisan [5], 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 Õ(N3/7).