Abstract
Senstivity and block sensitivity are important measures of complexity of Boolean functions. In this note we exhibit a Boolean function ofn variables that has sensitivity\(O(\sqrt n )\) and block sensitivity Ω(n). This demonstrates a quadratic separation of the two measures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. A. Cook, C. Dwork, andR. Reischuk: Upper and lower time bounds for parallel random access machines without simultaneous writes,SIAM J. Computing 15 (1986), 87–97.
Anna Gál: Lower bounds for the complexity of reliable Boolean circuits with noisy gates, in:32nd IEEE Symp. on Foundations of Computer Science, San Juan, Puerto Rico 1991, 594–601.
N. Nisan: CREW PRAM's and decision trees, in:Proc 21th ACM Symposium on Theory of Computing, Seattle WA, 1989, 327–335.
N. Nisan, andM. Szegedy: On the degree of Boolean functions as real polynomials, in:Proc. 24th ACM Symposium on Theory of Computing, Victoria, B.C., 1992, 462–467.
H. U. Simon: A tight Ω(loglogn) bound on the time for parallel RAM's to compute nondegenerate Boolean functions, in:FCT'83, Springer Lecture Notes in Computer Science158 (1983), 439–444.
I. Wegener:The complexity of Boolean functions, Wiley and Teubner, Stuttgart, 1987. See 373–410.
Additional information
c/o László Babai
Rights and permissions
About this article
Cite this article
Rubinstein, D. Sensitivity vs. block sensitivity of Boolean functions. Combinatorica 15, 297–299 (1995). https://doi.org/10.1007/BF01200762
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01200762