Chakraborty, Sourav - On the sensitivity of cyclically-invariant Boolean functions

dmtcs:552 - Discrete Mathematics & Theoretical Computer Science, December 4, 2011, Vol. 13 no. 4
On the sensitivity of cyclically-invariant Boolean functions

Authors: Chakraborty, Sourav

In this paper we construct a cyclically invariant Boolean function whose sensitivity is Theta(n(1/3)). This result answers two previously published questions. Turan (1984) asked if any Boolean function, invariant under some transitive group of permutations, has sensitivity Omega(root n). Kenyon and Kutin (2004) asked whether for a "nice" function the product of 0-sensitivity and 1-sensitivity is Omega(n). Our function answers both questions in the negative. We also prove that for minterm-transitive functions (a natural class of Boolean functions including our example) the sensitivity is Omega(n(1/3)). Hence for this class of functions sensitivity and block sensitivity are polynomially related.

Source : oai:HAL:hal-00990492v1
Volume: Vol. 13 no. 4
Published on: December 4, 2011
Submitted on: June 29, 2010
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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