Minterm-transitive functions with asymptotically smallest block sensitivity

Authors:
Kazuyuki Amano
Affiliations:
Department of Computer Science, Gunma University, 1-5-1 Tenjin, Kiryu, Gunma 376-8515, Japan
Venue:
Information Processing Letters
Year:
2011

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Note: Block sensitivity of minterm-transitive functions

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Abstract

In this note, we give an explicit construction of a minterm-transitive Boolean function with block sensitivity O(n^3^/^7). This removes a log-factor from the previously known bounds by Xiaoming Sun [Block sensitivity of weakly symmetric functions, Theoret. Comput. Sci. 384 (1) (2007) 87-91] and by Andrew Drucker [Block sensitivity of minterm-transitive functions, Theoret. Comput. Sci. 412 (41) (2011) 5796-5801]. Due to the matching lower bound by Drucker, it is shown that the minimum achievable block sensitivity for non-constant minterm-transitive function is @Q(n^3^/^7).